History of Euler polynomials $E_n$

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2026-09-16 11:22 bmatschke interactive tags: Appell sequence, Sheffer sequence. a tag is a family of tables, and these are the members of one. numberdb-data#111 asked for it; the membership is decided by the generating function each table gives, not by its title. a tag is a family of tables, and these are the members of one. numberdb-dat current reviewed
2026-09-12 15:22 bmatschke attached generate.py
2026-09-01 22:15 bmatschke attach each link to the name it follows, so the name is the link
2026-08-26 21:16 bmatschke generator the Euler polynomials
2026-08-26 21:15 bmatschke with claude-opus-5 interactive proposed from euler.yaml

What changed between 2026-09-12 15:22 and 2026-09-16 11:22

from line 41 (6 lines, 2 more than before) @@ -41,4 +41,6 @@
 - number theory - generating function+- Appell sequence+- Sheffer sequence Programs:   program-sage:
from line 50 (95 lines, 78 fewer than before) @@ -48,173 +50,95 @@
       \             # the next one after this table" Numbers:-- params:-    n: '0'-  number: '1'-- params:-    n: '1'-  number: x - 1/2-- params:-    n: '2'-  number: x^2 - x-- params:-    n: '3'-  number: x^3 - 3/2*x^2 + 1/4-- params:-    n: '4'-  number: x^4 - 2*x^3 + x-- params:-    n: '5'-  number: x^5 - 5/2*x^4 + 5/2*x^2 - 1/2-- params:-    n: '6'-  number: x^6 - 3*x^5 + 5*x^3 - 3*x-- params:-    n: '7'-  number: x^7 - 7/2*x^6 + 35/4*x^4 - 21/2*x^2 + 17/8-- params:-    n: '8'-  number: x^8 - 4*x^7 + 14*x^5 - 28*x^3 + 17*x-- params:-    n: '9'-  number: x^9 - 9/2*x^8 + 21*x^6 - 63*x^4 + 153/2*x^2 - 31/2-- params:-    n: '10'-  number: x^10 - 5*x^9 + 30*x^7 - 126*x^5 + 255*x^3 - 155*x-- params:-    n: '11'-  number: x^11 - 11/2*x^10 + 165/4*x^8 - 231*x^6 + 2805/4*x^4 - 1705/2*x^2 + 691/4-- params:-    n: '12'-  number: x^12 - 6*x^11 + 55*x^9 - 396*x^7 + 1683*x^5 - 3410*x^3 + 2073*x-- params:-    n: '13'-  number: x^13 - 13/2*x^12 + 143/2*x^10 - 1287/2*x^8 + 7293/2*x^6 - 22165/2*x^4 +-    26949/2*x^2 - 5461/2-- params:-    n: '14'-  number: x^14 - 7*x^13 + 91*x^11 - 1001*x^9 + 7293*x^7 - 31031*x^5 + 62881*x^3 --    38227*x-- params:-    n: '15'-  number: x^15 - 15/2*x^14 + 455/4*x^12 - 3003/2*x^10 + 109395/8*x^8 - 155155/2*x^6+  '0': '1'+  '1': x - 1/2+  '2': x^2 - x+  '3': x^3 - 3/2*x^2 + 1/4+  '4': x^4 - 2*x^3 + x+  '5': x^5 - 5/2*x^4 + 5/2*x^2 - 1/2+  '6': x^6 - 3*x^5 + 5*x^3 - 3*x+  '7': x^7 - 7/2*x^6 + 35/4*x^4 - 21/2*x^2 + 17/8+  '8': x^8 - 4*x^7 + 14*x^5 - 28*x^3 + 17*x+  '9': x^9 - 9/2*x^8 + 21*x^6 - 63*x^4 + 153/2*x^2 - 31/2+  '10': x^10 - 5*x^9 + 30*x^7 - 126*x^5 + 255*x^3 - 155*x+  '11': x^11 - 11/2*x^10 + 165/4*x^8 - 231*x^6 + 2805/4*x^4 - 1705/2*x^2 + 691/4+  '12': x^12 - 6*x^11 + 55*x^9 - 396*x^7 + 1683*x^5 - 3410*x^3 + 2073*x+  '13': x^13 - 13/2*x^12 + 143/2*x^10 - 1287/2*x^8 + 7293/2*x^6 - 22165/2*x^4 + 26949/2*x^2+    - 5461/2+  '14': x^14 - 7*x^13 + 91*x^11 - 1001*x^9 + 7293*x^7 - 31031*x^5 + 62881*x^3 - 38227*x+  '15': x^15 - 15/2*x^14 + 455/4*x^12 - 3003/2*x^10 + 109395/8*x^8 - 155155/2*x^6     + 943215/4*x^4 - 573405/2*x^2 + 929569/16-- params:-    n: '16'-  number: x^16 - 8*x^15 + 140*x^13 - 2184*x^11 + 24310*x^9 - 177320*x^7 + 754572*x^5+  '16': x^16 - 8*x^15 + 140*x^13 - 2184*x^11 + 24310*x^9 - 177320*x^7 + 754572*x^5     - 1529080*x^3 + 929569*x-- params:-    n: '17'-  number: x^17 - 17/2*x^16 + 170*x^14 - 3094*x^12 + 41327*x^10 - 376805*x^8 + 2137954*x^6+  '17': x^17 - 17/2*x^16 + 170*x^14 - 3094*x^12 + 41327*x^10 - 376805*x^8 + 2137954*x^6     - 6498590*x^4 + 15802673/2*x^2 - 3202291/2-- params:-    n: '18'-  number: x^18 - 9*x^17 + 204*x^15 - 4284*x^13 + 67626*x^11 - 753610*x^9 + 5497596*x^7+  '18': x^18 - 9*x^17 + 204*x^15 - 4284*x^13 + 67626*x^11 - 753610*x^9 + 5497596*x^7     - 23394924*x^5 + 47408019*x^3 - 28820619*x-- params:-    n: '19'-  number: x^19 - 19/2*x^18 + 969/4*x^16 - 5814*x^14 + 214149/2*x^12 - 1431859*x^10-    + 26113581/2*x^8 - 74083926*x^6 + 900752361/4*x^4 - 547591761/2*x^2 + 221930581/4-- params:-    n: '20'-  number: x^20 - 10*x^19 + 285*x^17 - 7752*x^15 + 164730*x^13 - 2603380*x^11 + 29015090*x^9+  '19': x^19 - 19/2*x^18 + 969/4*x^16 - 5814*x^14 + 214149/2*x^12 - 1431859*x^10 ++    26113581/2*x^8 - 74083926*x^6 + 900752361/4*x^4 - 547591761/2*x^2 + 221930581/4+  '20': x^20 - 10*x^19 + 285*x^17 - 7752*x^15 + 164730*x^13 - 2603380*x^11 + 29015090*x^9     - 211668360*x^7 + 900752361*x^5 - 1825305870*x^3 + 1109652905*x-- params:-    n: '21'-  number: x^21 - 21/2*x^20 + 665/2*x^18 - 20349/2*x^16 + 247095*x^14 - 4555915*x^12+  '21': x^21 - 21/2*x^20 + 665/2*x^18 - 20349/2*x^16 + 247095*x^14 - 4555915*x^12     + 60931689*x^10 - 555629445*x^8 + 6305266527/2*x^6 - 19165711635/2*x^4 + 23302711005/2*x^2     - 4722116521/2-- params:-    n: '22'-  number: x^22 - 11*x^21 + 385*x^19 - 13167*x^17 + 362406*x^15 - 7710010*x^13 + 121863378*x^11+  '22': x^22 - 11*x^21 + 385*x^19 - 13167*x^17 + 362406*x^15 - 7710010*x^13 + 121863378*x^11     - 1358205310*x^9 + 9908275971*x^7 - 42164565597*x^5 + 85443273685*x^3 - 51943281731*x-- params:-    n: '23'-  number: x^23 - 23/2*x^22 + 1771/4*x^20 - 33649/2*x^18 + 4167669/8*x^16 - 12666445*x^14+  '23': x^23 - 23/2*x^22 + 1771/4*x^20 - 33649/2*x^18 + 4167669/8*x^16 - 12666445*x^14     + 467142949/2*x^12 - 3123872213*x^10 + 227890347333/8*x^8 - 323261669577/2*x^6     + 1965195294755/4*x^4 - 1194695479813/2*x^2 + 968383680827/8-- params:-    n: '24'-  number: x^24 - 12*x^23 + 506*x^21 - 21252*x^19 + 735471*x^17 - 20266312*x^15 + 431208876*x^13+  '24': x^24 - 12*x^23 + 506*x^21 - 21252*x^19 + 735471*x^17 - 20266312*x^15 + 431208876*x^13     - 6815721192*x^11 + 75963449111*x^9 - 554162862132*x^7 + 2358234353706*x^5 - 4778781919252*x^3     + 2905151042481*x-- params:-    n: '25'-  number: x^25 - 25/2*x^24 + 575*x^22 - 26565*x^20 + 2042975/2*x^18 - 63332225/2*x^16+  '25': x^25 - 25/2*x^24 + 575*x^22 - 26565*x^20 + 2042975/2*x^18 - 63332225/2*x^16     + 770015850*x^14 - 14199419150*x^12 + 379817245555/2*x^10 - 3463517888325/2*x^8     + 9825976473775*x^6 - 29867386995325*x^4 + 72628776062025/2*x^2 - 14717667114151/2-- params:-    n: '26'-  number: x^26 - 13*x^25 + 650*x^23 - 32890*x^21 + 1397825*x^19 - 48430525*x^17 +-    1334694140*x^15 - 28398838300*x^13 + 448874926565*x^11 - 5002859172025*x^9 + 36496484045450*x^7+  '26': x^26 - 13*x^25 + 650*x^23 - 32890*x^21 + 1397825*x^19 - 48430525*x^17 + 1334694140*x^15+    - 28398838300*x^13 + 448874926565*x^11 - 5002859172025*x^9 + 36496484045450*x^7     - 155310412375690*x^5 + 314724696268775*x^3 - 191329672483963*x-- params:-    n: '27'-  number: x^27 - 27/2*x^26 + 2925/4*x^24 - 40365*x^22 + 7548255/4*x^20 - 145291575/2*x^18+  '27': x^27 - 27/2*x^26 + 2925/4*x^24 - 40365*x^22 + 7548255/4*x^20 - 145291575/2*x^18     + 9009185445/4*x^16 - 54769188150*x^14 + 4039874339085/4*x^12 - 27015439528935/2*x^10     + 492702534613575/4*x^8 - 698896855690605*x^6 + 8497566799256925/4*x^4 - 5165901157067001/2*x^2     + 2093660879252671/4-- params:-    n: '28'-  number: x^28 - 14*x^27 + 819*x^25 - 49140*x^23 + 2516085*x^21 - 107056950*x^19 +-    3709664595*x^17 - 102235817880*x^15 + 2175316951815*x^13 - 34383286673190*x^11-    + 383213082477225*x^9 - 2795587422762420*x^7 + 11896593518959695*x^5 - 24107538732979338*x^3-    + 14655626154768697*x-- params:-    n: '29'-  number: x^29 - 29/2*x^28 + 1827/2*x^26 - 118755/2*x^24 + 6633315/2*x^22 - 310465155/2*x^20+  '28': x^28 - 14*x^27 + 819*x^25 - 49140*x^23 + 2516085*x^21 - 107056950*x^19 + 3709664595*x^17+    - 102235817880*x^15 + 2175316951815*x^13 - 34383286673190*x^11 + 383213082477225*x^9+    - 2795587422762420*x^7 + 11896593518959695*x^5 - 24107538732979338*x^3 + 14655626154768697*x+  '29': x^29 - 29/2*x^28 + 1827/2*x^26 - 118755/2*x^24 + 6633315/2*x^22 - 310465155/2*x^20     + 11953363695/2*x^18 - 370604839815/2*x^16 + 9012027371805/2*x^14 - 166185885587085/2*x^12     + 2222635878367905/2*x^10 - 20268008815027545/2*x^8 + 115000404016610385/2*x^6     - 349559311628200401/2*x^4 + 425013158488292213/2*x^2 - 86125672563201181/2-- params:-    n: '30'-  number: x^30 - 15*x^29 + 1015*x^27 - 71253*x^25 + 4326075*x^23 - 221760825*x^21-    + 9436866075*x^19 - 327004270425*x^17 + 9012027371805*x^15 - 191752944908175*x^13+  '30': x^30 - 15*x^29 + 1015*x^27 - 71253*x^25 + 4326075*x^23 - 221760825*x^21 ++    9436866075*x^19 - 327004270425*x^17 + 9012027371805*x^15 - 191752944908175*x^13     + 3030867106865325*x^11 - 33780014691712575*x^9 + 246429437178450825*x^7 - 1048677934884601203*x^5     + 2125065792441461065*x^3 - 1291885088448017715*x-- params:-    n: '31'-  number: x^31 - 31/2*x^30 + 4495/4*x^28 - 169911/2*x^26 + 44702775/8*x^24 - 624962325/2*x^22+  '31': x^31 - 31/2*x^30 + 4495/4*x^28 - 169911/2*x^26 + 44702775/8*x^24 - 624962325/2*x^22     + 58508569665/4*x^20 - 1126348042575/2*x^18 + 279372848525955/16*x^16 - 849191613164775/2*x^14     + 31318960104275025/4*x^12 - 209436091088617965/2*x^10 + 7639312552531975575/8*x^8     - 10836338660474212431/2*x^6 + 65877039565685293015/4*x^4 - 40048437741888549165/2*x^2     + 129848163681107301953/32-- params:-    n: '32'-  number: x^32 - 16*x^31 + 1240*x^29 - 100688*x^27 + 7152444*x^25 - 434756400*x^23-    + 22288978920*x^21 - 948503614800*x^19 + 32867393944230*x^17 - 905804387375760*x^15+  '32': x^32 - 16*x^31 + 1240*x^29 - 100688*x^27 + 7152444*x^25 - 434756400*x^23 ++    22288978920*x^21 - 948503614800*x^19 + 32867393944230*x^17 - 905804387375760*x^15     + 19273206218015400*x^13 - 304634314310717040*x^11 + 3395250023347544700*x^9 -     24768774081083914128*x^7 + 105403263305096468824*x^5 - 213591667956738928880*x^3     + 129848163681107301953*x-- params:-    n: '33'-  number: x^33 - 33/2*x^32 + 1364*x^30 - 118668*x^28 + 9078102*x^26 - 597790050*x^24+  '33': x^33 - 33/2*x^32 + 1364*x^30 - 118668*x^28 + 9078102*x^26 - 597790050*x^24     + 33433468380*x^22 - 1565030964420*x^20 + 60256888897755*x^18 - 1868221548962505*x^16     + 45429700371036300*x^14 - 837744364354471860*x^12 + 11204325077046897510*x^10     - 102171193084471145778*x^8 + 579717948178030578532*x^6 - 1762131260643096163260*x^4     + 4284989401476540964449/2*x^2 - 868320396104950823611/2-- params:-    n: '34'-  number: x^34 - 17*x^33 + 1496*x^31 - 139128*x^29 + 11431684*x^27 - 812994468*x^25+  '34': x^34 - 17*x^33 + 1496*x^31 - 139128*x^29 + 11431684*x^27 - 812994468*x^25     + 49423388040*x^23 - 2533859656680*x^21 + 107828116974930*x^19 - 3736443097925010*x^17     + 102973987507682280*x^15 - 2191023722157849480*x^13 + 34631550238144955940*x^11     - 385980062763557661828*x^9 + 2815772891150434238584*x^7 - 11982492572373053910168*x^5     + 24281606608367065465211*x^3 - 14761446733784164001387*x-- params:-    n: '35'-  number: x^35 - 35/2*x^34 + 6545/4*x^32 - 162316*x^30 + 14289605*x^28 - 1094415630*x^26+  '35': x^35 - 35/2*x^34 + 6545/4*x^32 - 162316*x^30 + 14289605*x^28 - 1094415630*x^26     + 72075774225*x^24 - 4031140362900*x^22 + 377398409412255/2*x^20 - 7265306023743075*x^18     + 450511195346109975/2*x^16 - 5477559305394623700*x^14 + 101008688194589454825*x^12     - 1350930219672451816398*x^10 + 12319006398783149793805*x^8 - 69897873338842814475980*x^6     + 849856231292847291282385/4*x^4 - 516650635682445740048545/2*x^2 + 209390615747646519456961/4-- params:-    n: '36'-  number: x^36 - 18*x^35 + 1785*x^33 - 188496*x^31 + 17738820*x^29 - 1459220840*x^27+  '36': x^36 - 18*x^35 + 1785*x^33 - 188496*x^31 + 17738820*x^29 - 1459220840*x^27     + 103789114884*x^25 - 6309611002800*x^23 + 323484350924790*x^21 - 13765842992355300*x^19     + 477011853895881150*x^17 - 13146142332947096880*x^15 + 279716367308093874900*x^13     - 4421226173473478671848*x^11 + 49276025595132599175220*x^9 - 359474777171191617305040*x^7     + 1529741216327125124308293*x^5 - 3099903814094674440291270*x^3 + 1884515541728818675112649*x-- params:-    n: '37'-  number: x^37 - 37/2*x^36 + 3885/2*x^34 - 435897/2*x^32 + 21877878*x^30 - 1928256110*x^28+  '37': x^37 - 37/2*x^36 + 3885/2*x^34 - 435897/2*x^32 + 21877878*x^30 - 1928256110*x^28     + 147699894258*x^26 - 9727316962650*x^24 + 544041862918965*x^22 - 25466809535857305*x^20     + 980524366341533475*x^18 - 30400454144940161535*x^16 + 739250399314248097950*x^14
from line 146 (5 lines, 2 fewer than before) @@ -222,7 +146,5 @@
     + 18866808334701209866468947/2*x^6 - 57348220560751477145388495/2*x^4 + 69727075043966290979168013/2*x^2     - 14129659550745551130667441/2-- params:-    n: '38'-  number: x^38 - 19*x^37 + 2109*x^35 - 250971*x^33 + 26818044*x^31 - 2526680420*x^29+  '38': x^38 - 19*x^37 + 2109*x^35 - 250971*x^33 + 26818044*x^31 - 2526680420*x^29     + 207873925252*x^27 - 14785521783228*x^25 + 898851773518290*x^23 - 46082798207741790*x^21     + 1961048732683066950*x^19 - 67953956323983890490*x^17 + 1872767678262761848140*x^15
from line 152 (5 lines, 2 fewer than before) @@ -230,7 +152,5 @@
     + 51209908337046141066129999*x^7 - 217923238130855613152476281*x^5 + 441604808611786509534730749*x^3     - 268463531464165471482681379*x-- params:-    n: '39'-  number: x^39 - 39/2*x^38 + 9139/4*x^36 - 575757/2*x^34 + 261475929/8*x^32 - 3284684546*x^30+  '39': x^39 - 39/2*x^38 + 9139/4*x^36 - 575757/2*x^34 + 261475929/8*x^32 - 3284684546*x^30     + 289538681601*x^28 - 22178282674842*x^26 + 5842536527868885/4*x^24 - 81692233186451355*x^22     + 7648090057463961105/2*x^20 - 147233572035298429395*x^18 + 18259484863061928019365/4*x^16
from line 158 (5 lines, 2 fewer than before) @@ -238,7 +158,5 @@
     + 1997186425144799501579069961/8*x^8 - 2833002095701122970982191653/2*x^6 + 17222587535859673871854499211/4*x^4     - 10470077727102453387824573781/2*x^2 + 8486725345098385062639014237/8-- params:-    n: '40'-  number: x^40 - 20*x^39 + 2470*x^37 - 329004*x^35 + 39617565*x^33 - 4238302640*x^31+  '40': x^40 - 20*x^39 + 2470*x^37 - 329004*x^35 + 39617565*x^33 - 4238302640*x^31     + 399363698760*x^29 - 32856715073840*x^27 + 2337014611147554*x^25 - 142073449019915400*x^23     + 7283895292822820100*x^21 - 309965414811154588200*x^19 + 10740873448859957658450*x^17
from line 164 (5 lines, 2 fewer than before) @@ -246,7 +164,5 @@
     + 1109548013969333056432816645*x^9 - 8094291702003208488520547580*x^7 + 34445175071719347743708998422*x^5     - 69800518180683022585497158540*x^3 + 42433626725491925313195071185*x-- params:-    n: '41'-  number: x^41 - 41/2*x^40 + 2665*x^38 - 374699*x^36 + 95548245/2*x^34 - 10860650515/2*x^32+  '41': x^41 - 41/2*x^40 + 2665*x^38 - 374699*x^36 + 95548245/2*x^34 - 10860650515/2*x^32     + 545797054972*x^30 - 48111618500980*x^28 + 3685292271424989*x^26 - 242708808742355475*x^24     + 13574532136624346550*x^22 - 635429100362866905810*x^20 + 24465322855736570222025*x^18
from line 171 (5 lines, 2 fewer than before) @@ -255,7 +171,5 @@
     235375362990082209582011489217*x^6 - 715455311352000981501345875035*x^4 + 1739778695745168937840997918585/2*x^2     - 352552873457246307069012458671/2-- params:-    n: '42'-  number: x^42 - 21*x^41 + 2870*x^39 - 425334*x^37 + 57328947*x^35 - 6911323055*x^33+  '42': x^42 - 21*x^41 + 2870*x^39 - 425334*x^37 + 57328947*x^35 - 6911323055*x^33     + 739466977704*x^31 - 69678895760040*x^29 + 5732676866661094*x^27 - 407750798687157198*x^25     + 24788276075574893700*x^23 - 1270858200725733811620*x^21 + 54081239996891365753950*x^19
from line 178 (5 lines, 2 fewer than before) @@ -264,7 +178,5 @@
     - 6009824615356808244611305350294*x^5 + 12178450870216182564886985430095*x^3 -     7403610342602172448449261632091*x-- params:-    n: '43'-  number: x^43 - 43/2*x^42 + 12341/4*x^40 - 481299*x^38 + 273904969/4*x^36 - 17481581845/2*x^34+  '43': x^43 - 43/2*x^42 + 12341/4*x^40 - 481299*x^38 + 273904969/4*x^36 - 17481581845/2*x^34     + 3974635005159/4*x^32 - 99873083922724*x^30 + 17607507519030503/2*x^28 - 674357090136452289*x^26     + 88824655937476702425/2*x^24 - 2483950119600297904530*x^22 + 232549331986632872741985/2*x^20
from line 186 (5 lines, 2 fewer than before) @@ -274,7 +186,5 @@
     + 523673387419295850290140373494085/4*x^4 - 318355244731893415283318250179913/2*x^2     + 129024520859926228378837238913451/4-- params:-    n: '44'-  number: x^44 - 22*x^43 + 3311*x^41 - 543004*x^39 + 81431207*x^37 - 10988422874*x^35+  '44': x^44 - 22*x^43 + 3311*x^41 - 543004*x^39 + 81431207*x^37 - 10988422874*x^35     + 1324878335053*x^33 - 141755344922576*x^31 + 13357419497195554*x^29 - 1098952295037181508*x^27     + 78165697224979498134*x^25 - 4751904576626656860840*x^23 + 243623109700282057158270*x^21
from line 194 (5 lines, 2 fewer than before) @@ -284,7 +194,5 @@
     1152081452322450870638308821686987*x^5 - 2334605128033885045411000501319362*x^3     + 1419269729459188512167209628047961*x-- params:-    n: '45'-  number: x^45 - 45/2*x^44 + 7095/2*x^42 - 1221759/2*x^40 + 192863385/2*x^38 - 27471057185/2*x^36+  '45': x^45 - 45/2*x^44 + 7095/2*x^42 - 1221759/2*x^40 + 192863385/2*x^38 - 27471057185/2*x^36     + 3507030886905/2*x^34 - 398686907594745/2*x^32 + 20036129245793331*x^30 - 1766173331309755995*x^28     + 135286783658618362155*x^26 - 8909821081174981614075*x^24 + 498319997114213298732825*x^22
from line 202 (5 lines, 2 fewer than before) @@ -294,7 +202,5 @@
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from line 210 (5 lines, 2 fewer than before) @@ -304,7 +210,5 @@
     + 56781157293035078624316649068858645*x^7 - 241631630751507102200038551886553967*x^5     + 489648056663420036697687321676546545*x^3 - 297670324015849154718455710038555923*x-- params:-    n: '47'-  number: x^47 - 47/2*x^46 + 16215/4*x^44 - 1533939/2*x^42 + 1069155483/8*x^40 - 42242123495/2*x^38+  '47': x^47 - 47/2*x^46 + 16215/4*x^44 - 1533939/2*x^42 + 1069155483/8*x^40 - 42242123495/2*x^38     + 12035239329347/4*x^36 - 768236269358145/2*x^34 + 698679216603309381/16*x^32     - 4389042232519186737*x^30 + 773783138280245764495/2*x^28 - 29635435657692784999431*x^26
from line 219 (5 lines, 2 fewer than before) @@ -315,7 +219,5 @@
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from line 228 (5 lines, 2 fewer than before) @@ -326,7 +228,5 @@
     + 55232300791633780139499129885114450276*x^5 - 111924041829959282174139346974497027048*x^3     + 68041658377475993470566379406771713377*x-- params:-    n: '49'-  number: x^49 - 49/2*x^48 + 4606*x^46 - 953442*x^44 + 182538741*x^42 - 31844062327*x^40+  '49': x^49 - 49/2*x^48 + 4606*x^46 - 953442*x^44 + 182538741*x^42 - 31844062327*x^40     + 5033229534606*x^38 - 717020518067602*x^36 + 183076372265038287/2*x^34 - 20812555102590982269/2*x^32     + 1045941345537435654076*x^30 - 92199133157266442220452*x^28 + 7062344328332512166041206*x^26
from line 237 (5 lines, 2 fewer than before) @@ -337,7 +237,5 @@
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