History of Bernoulli polynomials of the second kind $\psi_n$

        series[26] * factorial(26)       # the next one after this table'-Numbers: []+Numbers:+- params:+    n: '0'+  number: '1'+- params:+    n: '1'+  number: x + 1/2+- params:+    n: '2'+  number: x^2 - 1/6+- params:+    n: '3'+  number: x^3 - 3/2*x^2 + 1/4+- params:+    n: '4'+  number: x^4 - 4*x^3 + 4*x^2 - 19/30+- params:+    n: '5'+  number: x^5 - 15/2*x^4 + 55/3*x^3 - 15*x^2 + 9/4+- params:+    n: '6'+  number: x^6 - 12*x^5 + 105/2*x^4 - 100*x^3 + 72*x^2 - 863/84+- params:+    n: '7'+  number: x^7 - 35/2*x^6 + 119*x^5 - 1575/4*x^4 + 1918/3*x^3 - 420*x^2 + 1375/24+- params:+    n: '8'+  number: x^8 - 24*x^7 + 700/3*x^6 - 1176*x^5 + 3248*x^4 - 4704*x^3 + 2880*x^2 - 33953/90+- params:+    n: '9'+  number: x^9 - 63/2*x^8 + 414*x^7 - 2940*x^6 + 60921/5*x^5 - 29547*x^4 + 39204*x^3+    - 22680*x^2 + 57281/20+- params:+    n: '10'+  number: x^10 - 40*x^9 + 1365/2*x^8 - 6480*x^7 + 37415*x^6 - 134568*x^5 + 295310*x^4+    - 365280*x^3 + 201600*x^2 - 3250433/132+- params:+    n: '11'+  number: x^11 - 99/2*x^10 + 3190/3*x^9 - 51975/4*x^8 + 99429*x^7 - 987525/2*x^6 ++    1592096*x^5 - 3224925*x^4 + 3764112*x^3 - 1995840*x^2 + 1891755/8+- params:+    n: '12'+  number: x^12 - 60*x^11 + 1584*x^10 - 24200*x^9 + 473319/2*x^8 - 1546380*x^7 + 6833860*x^6+    - 20182800*x^5 + 38260728*x^4 - 42514560*x^3 + 21772800*x^2 - 13695779093/5460+- params:+    n: '13'+  number: x^13 - 143/2*x^12 + 2275*x^11 - 42471*x^10 + 1548833/3*x^9 - 17144127/4*x^8+    + 173413955/7*x^7 - 99657415*x^6 + 1368354988/5*x^5 - 490483422*x^4 + 522356640*x^3+    - 259459200*x^2 + 24466579093/840+- params:+    n: '14'+  number: x^14 - 84*x^13 + 19019/6*x^12 - 70980*x^11 + 5246241/5*x^10 - 10774764*x^9+    + 314931617/4*x^8 - 412140300*x^7 + 4600447852/3*x^6 - 19796208432/5*x^5 + 6760458432*x^4+    - 6936733440*x^3 + 3353011200*x^2 - 132282840127/360+- params:+    n: '15'+  number: x^15 - 195/2*x^14 + 4305*x^13 - 455455/4*x^12 + 2010645*x^11 - 50008959/2*x^10+    + 675182365/3*x^9 - 11864147295/8*x^8 + 7148825970*x^7 - 24894259390*x^6 + 60941259288*x^5+    - 99737688960*x^4 + 99013795200*x^3 - 46702656000*x^2 + 240208245823/48+- params:+    n: '16'+  number: x^16 - 112*x^15 + 5720*x^14 - 176400*x^13 + 10998988/3*x^12 - 54272400*x^11+    + 589458584*x^10 - 14301086800/3*x^9 + 28818645856*x^8 - 129516266880*x^7 + 1277772845440/3*x^6+    - 995165633280*x^5 + 1568627191296*x^4 - 1511816785920*x^3 + 697426329600*x^2+    - 111956703448001/1530+- params:+    n: '17'+  number: x^17 - 255/2*x^16 + 22372/3*x^15 - 265200*x^14 + 6407198*x^13 - 111291180*x^12+    + 1434329780*x^11 - 13952967600*x^10 + 928729202401/9*x^9 - 579706822695*x^8 ++    2452060831480*x^7 - 7669304479200*x^6 + 85968926965008/5*x^5 - 26204724862560*x^4+    + 24588590342400*x^3 - 11115232128000*x^2 + 4573423873125/4+- params:+    n: '18'+  number: x^18 - 144*x^17 + 19125/2*x^16 - 388416*x^15 + 10792314*x^14 - 217318752*x^13+    + 3277547130*x^12 - 37729897920*x^11 + 1673578597977/5*x^10 - 2293802567056*x^9+    + 12092677825410*x^8 - 48501172437120*x^7 + 145098027700272*x^6 - 1567399479766272/5*x^5+    + 463465101767040*x^4 - 424405694361600*x^3 + 188305108992000*x^2 - 30342376302478019/1596+- params:+    n: '19'+  number: x^19 - 323/2*x^18 + 12084*x^17 - 2223855/4*x^16 + 88011686/5*x^15 - 406668951*x^14+    + 7093171732*x^13 - 95320932135*x^12 + 998233909257*x^11 - 81854000736651/10*x^10+    + 157521686886928/3*x^9 - 261792607187475*x^8 + 7011240335453296/7*x^7 - 2879449701839688*x^6+    + 30082965538822272/5*x^5 - 8652611611967040*x^4 + 7748235407001600*x^3 - 3379030566912000*x^2+    + 56310194579604163/168+- params:+    n: '20'+  number: x^20 - 180*x^19 + 45220/3*x^18 - 779760*x^17 + 55809555/2*x^16 - 733052376*x^15+    + 102469372720/7*x^14 - 227016467280*x^13 + 2769288977455*x^12 - 26746824379860*x^11+    + 204835481465316*x^10 - 1239825958993440*x^9 + 5882812601374960*x^8 - 151030551841260480/7*x^7+    + 59835707603071680*x^6 - 121285016030877696*x^5 + 170061247969113600*x^4 - 149179920390144000*x^3+    + 64023737057280000*x^2 - 12365722323469980029/1980+- params:+    n: '21'+  number: x^21 - 399/2*x^20 + 18585*x^19 - 1073975*x^18 + 43132698*x^17 - 5113194975/4*x^16+    + 28970107082*x^15 - 513378767850*x^14 + 7213058608077*x^13 - 161982267131685/2*x^12+    + 8020363165546095/11*x^11 - 5258103386481855*x^10 + 90675458929607272/3*x^9 -+    137184871326595890*x^8 + 484289209590356880*x^7 - 1299846755708298000*x^6 + 12812437590550327296/5*x^5+    - 3510201084291054720*x^4 + 3020956027723468800*x^3 - 1277273554292736000*x^2+    + 161867055619224199787/1320+- params:+    n: '22'+  number: x^22 - 220*x^21 + 45353/2*x^20 - 1455300*x^19 + 195535802/3*x^18 - 2164128120*x^17+    + 220944743965/4*x^16 - 1108963070600*x^15 + 17773292421313*x^14 - 229451847983820*x^13+    + 4794295038648115/2*x^12 - 20284599731022900*x^11 + 693338933092243856/5*x^10+    - 2283113383183531360/3*x^9 + 3318281460396026740*x^8 - 11314221342121051200*x^7+    + 29471976683031856512*x^6 - 56632097478664350720*x^5 + 75920678645023872000*x^4+    - 64188285602918400000*x^3 + 26761922089943040000*x^2 - 20953816286242674495191/8280+- params:+    n: '23'+  number: x^23 - 483/2*x^22 + 82225/3*x^21 - 7772919/4*x^20 + 96505332*x^19 - 3567769821*x^18+    + 101862493150*x^17 - 18396761470395/8*x^16 + 625338073007263/15*x^15 - 1225903285065459/2*x^14+    + 7350842198684775*x^13 - 288270768999258045/4*x^12 + 577130864847801178*x^11+    - 18802278018335709744/5*x^10 + 178127049133900266400/9*x^9 - 83201302267339412310*x^8+    + 274808539869932924064*x^7 - 696382421496005458368*x^6 + 1306829253148332756480*x^5+    - 1717133441463494208000*x^4 + 1427876882647971840000*x^3 - 587545834974658560000*x^2+    + 4380881778942163832799/80+- params:+    n: '24'+  number: x^24 - 264*x^23 + 32844*x^22 - 2560360*x^21 + 701379756/5*x^20 - 5742375408*x^19+    + 546869431768/3*x^18 - 4596834498960*x^17 + 187147249265823/2*x^16 - 7770003687519304/5*x^15+    + 21193792880719212*x^14 - 238166141203073160*x^13 + 2206461762371899472*x^12+    - 16816147857376060512*x^11 + 524570755795132953984/5*x^10 - 1594575825768529098880/3*x^9+    + 2160924649322773961088*x^8 - 6931499577979483685376*x^7 + 17122891461428588571648*x^6+    - 31433687292974729748480*x^5 + 40536880042625584128000*x^4 - 33187814234683637760000*x^3+    + 13488008733331292160000*x^2 - 101543126947618093900697699/81900+- params:+    n: '25'+  number: x^25 - 575/2*x^24 + 39050*x^23 - 3332700*x^22 + 601513825/3*x^21 - 9043336995*x^20+    + 317469004600*x^19 - 26669126400400/3*x^18 + 201871340883575*x^17 - 15037787741528475/4*x^16+    + 173509032243521030/3*x^15 - 738136989823775100*x^14 + 101759601425189238025/13*x^13+    - 68920232017862927075*x^12 + 502237397680531175900*x^11 - 3011873150404344081240*x^10+    + 132617842888136145324400/9*x^9 - 58089926109537343051800*x^8 + 1269488313357571254974400/7*x^7+    - 437522128149656054102400*x^6 + 786879491429707553664000*x^5 - 997124064225417878400000*x^4+    + 804491388770775552000000*x^3 - 323150209236062208000000*x^2 + 192060902780872132330221667/6552