History of Stirling convolution polynomials $\sigma_n(x)$

 Display properties:   number-header: $\sigma_n(x)$-Numbers: []+Numbers:+- params:+    n: '1'+  number: 1/2+- params:+    n: '2'+  number: 1/8*x - 1/24+- params:+    n: '3'+  number: 1/48*x^2 - 1/48*x+- params:+    n: '4'+  number: 1/384*x^3 - 1/192*x^2 + 1/1152*x + 1/2880+- params:+    n: '5'+  number: 1/3840*x^4 - 1/1152*x^3 + 1/2304*x^2 + 1/5760*x+- params:+    n: '6'+  number: 1/46080*x^5 - 1/9216*x^4 + 1/9216*x^3 + 13/414720*x^2 - 1/69120*x - 1/181440+- params:+    n: '7'+  number: 1/645120*x^6 - 1/92160*x^5 + 1/55296*x^4 + 1/829440*x^3 - 1/138240*x^2 -+    1/362880*x+- params:+    n: '8'+  number: 1/10321920*x^7 - 1/1105920*x^6 + 1/442368*x^5 - 1/1658880*x^4 - 67/39813120*x^3+    - 1/2580480*x^2 + 101/348364800*x + 1/9676800+- params:+    n: '9'+  number: 1/185794560*x^8 - 1/15482880*x^7 + 1/4423680*x^6 - 1/6220800*x^5 - 19/79626240*x^4+    + 1/27869184*x^3 + 101/696729600*x^2 + 1/19353600*x+- params:+    n: '10'+  number: 1/3715891200*x^9 - 1/247726080*x^8 + 1/53084160*x^7 - 19/796262400*x^6 -+    7/318504960*x^5 + 149/6688604160*x^4 + 67/2090188800*x^3 + 47/8360755200*x^2 -+    13/2090188800*x - 1/479001600+- params:+    n: '11'+  number: 1/81749606400*x^10 - 1/4459069440*x^9 + 1/743178240*x^8 - 29/11147673600*x^7+    - 11/9555148800*x^6 + 289/66886041600*x^5 + 11/2786918400*x^4 - 1/668860416*x^3+    - 13/4180377600*x^2 - 1/958003200*x+- params:+    n: '12'+  number: 1/1961990553600*x^11 - 1/89181388800*x^10 + 1/11890851840*x^9 - 61/267544166400*x^8+    + 1/76441190400*x^7 + 143/267544166400*x^6 + 1151/4815794995200*x^5 - 481/802632499200*x^4+    - 793/1203948748800*x^3 - 311/3678732288000*x^2 + 7999/57940033536000*x + 691/15692092416000+- params:+    n: '13'+  number: 1/51011754393600*x^12 - 1/1961990553600*x^11 + 1/214035333120*x^10 - 1/59454259200*x^9+    + 11/1070176665600*x^8 + 541/11236854988800*x^7 - 389/48157949952000*x^6 - 829/8026324992000*x^5+    - 169/2407897497600*x^4 + 47/1051066368000*x^3 + 7999/115880067072000*x^2 + 691/31384184832000*x+- params:+    n: '14'+  number: 1/1428329123020800*x^13 - 1/47087773286400*x^12 + 1/4280706662400*x^11 -+    23/21403533312000*x^10 + 17/12842119987200*x^9 + 59/17978967982080*x^8 - 713/192631799808000*x^7+    - 937/82556485632000*x^6 - 11/6421059993600*x^5 + 24151/1589212348416000*x^4 ++    8689/618027024384000*x^3 + 22271/18077290463232000*x^2 - 2357/753220435968000*x+    - 1/1046139494400+- params:+    n: '15'+  number: 1/42849873690624000*x^14 - 1/1224282105446400*x^13 + 1/94175546572800*x^12+    - 257/4237899595776000*x^11 + 1/8561413324800*x^10 + 89/539369039462400*x^9 -+    3959/8090535591936000*x^8 - 6901/8090535591936000*x^7 + 389/577895399424000*x^6+    + 7699/3178424696832000*x^5 + 14209/11124486438912000*x^4 - 1259/1032988026470400*x^3+    - 2357/1506440871936000*x^2 - 1/2092278988800*x+- params:+    n: '16'+  number: 1/1371195958099968000*x^15 - 1/34279898952499200*x^14 + 1/2260213117747200*x^13+    - 13/4237899595776000*x^12 + 17/2054739197952000*x^11 + 1/199766310912000*x^10+    - 2837/64724284735488000*x^9 - 13/323621423677440*x^8 + 2047/15850845241344000*x^7+    + 1043/4358982441369600*x^6 - 28691/1067950698135552000*x^5 - 130943/347083976894054400*x^4+    - 10662539/34708397689405440000*x^3 - 5281/333734593167360000*x^2 + 52037/723091618529280000*x+    + 3617/170729965486080000+- params:+    n: '17'+  number: 1/46620662575398912000*x^16 - 1/1028396968574976000*x^15 + 1/58765541061427200*x^14+    - 31/220370778980352000*x^13 + 29/58119765884928000*x^12 - 1/14832648585216000*x^11+    - 131/43149523156992000*x^10 - 29/97086427103232000*x^9 + 21487/1553382833651712000*x^8+    + 153859/10679506981355520000*x^7 - 256303/10679506981355520000*x^6 - 12731/225379205775360000*x^5+    - 32891/1416669293445120000*x^4 + 25177/788827220213760000*x^3 + 52037/1446183237058560000*x^2+    + 3617/341459930972160000*x+- params:+    n: '18'+  number: 1/1678343852714360832000*x^17 - 1/32908702994399232000*x^16 + 1/1645435149719961600*x^15+    - 437/74044581737398272000*x^14 + 43/1627353444777984000*x^13 - 263/11391474113445888000*x^12+    - 1319/7766914168258560000*x^11 + 1201/7766914168258560000*x^10 + 2189/2071177111535616000*x^9+    + 2265503/9227094031891169280000*x^8 - 235759/64077041888133120000*x^7 - 25040803/4998009267274383360000*x^6+    + 530941/277667181515243520000*x^5 + 473129/51000094564024320000*x^4 + 9473/1388335907576217600*x^3+    + 7132679/55759040888029839360000*x^2 - 1295681/774431123444858880000*x - 43867/91963695909076992000+- params:+    n: '19'+  number: 1/63777066403145711616000*x^18 - 1/1118895901809573888000*x^17 + 1/49363054491598848000*x^16+    - 13/56957370567229440000*x^15 + 53/42311189564227584000*x^14 - 73/35541399233951170560*x^13+    - 1319/170872111701688320000*x^12 + 3131/170872111701688320000*x^11 + 2263/37281188007641088000*x^10+    - 1019281/18454188063782338560000*x^9 - 6511/18689137217372160000*x^8 - 1391087/6361102703803760640000*x^7+    + 170827/238000441298780160000*x^6 + 1314421/999601853454876672000*x^5 + 869/2103539253903360000*x^4+    - 7023661/8578313982773821440000*x^3 - 1295681/1548862246889717760000*x^2 - 43867/183927391818153984000*x+- params:+    n: '20'+  number: 1/2551082656125828464640000*x^19 - 1/40280252465144659968000*x^18 + 1/1579617743731163136000*x^17+    - 97/11847133077983723520000*x^16 + 383/7108279846790234112000*x^15 - 3281/24878979463765819392000*x^14+    - 751/2733953787227013120000*x^13 + 5639/4100930680840519680000*x^12 + 3779/1491247520305643520000*x^11+    - 82483/10545250322161336320000*x^10 - 71800261/3100303594715432878080000*x^9+    + 417371/49757958927531638784000*x^8 + 3335117/34272063547024343040000*x^7 + 1384769/13328024712731688960000*x^6+    - 1216651/17136031773512171520000*x^5 - 40520646403/178428930841695485952000000*x^4+    - 513310799/3345542453281790361600000*x^3 + 24989087/14125623691634225971200000*x^2+    + 152388293/3884546515199412142080000*x + 174611/16057153253965824000000+- params:+    n: '21'+  number: 1/107145471557284795514880000*x^20 - 1/1530649593675497078784000*x^19 ++    1/53707003286859546624000*x^18 - 331/1208407573954339799040000*x^17 + 151/71082798467902341120000*x^16+    - 1747/248789794637658193920000*x^15 - 4099/639745186211121070080000*x^14 + 7/87040161389268172800*x^13+    + 5767/98422336340172472320000*x^12 - 3118319/4871905648838537379840000*x^11 -+    6516997/6200607189430865756160000*x^10 + 6636713/2686929782086708494336000*x^9+    + 140007961/16793311138041928089600000*x^8 + 21034703/8396655569020964044800000*x^7+    - 23931041/1199522224145852006400000*x^6 - 32765421289/1070573585050172915712000000*x^5+    - 46865639/6691084906563580723200000*x^4 + 586486687/28251247383268451942400000*x^3+    + 152388293/7769093030398824284160000*x^2 + 174611/32114306507931648000000*x+- params:+    n: '22'+  number: 1/4714400748520531002654720000*x^21 - 1/61225983747019883151360000*x^20+    + 1/1933452118326943678464000*x^19 - 83/9667260591634718392320000*x^18 + 1/12924145175982243840000*x^17+    - 1949/5970955071303796654080000*x^16 + 41/1628442292173762723840000*x^15 + 23273/5970955071303796654080000*x^14+    - 599/393689345360689889280000*x^13 - 7601791/194876225953541495193600000*x^12+    - 2698721/124012143788617315123200000*x^11 + 174715687/690924801108010755686400000*x^10+    + 1151822417/2418236803878037644902400000*x^9 - 99961079/201519733656503137075200000*x^8+    - 17846993/7197133344875112038400000*x^7 - 2022508057/951620964489042591744000000*x^6+    + 288529211/129766495157596717056000000*x^5 + 33855195523/6102269434785985619558400000*x^4+    + 116927697319/33562481891322920907571200000*x^3 - 23163719/166480564937117663232000000*x^2+    - 269839961/291340988639955910656000000*x - 77683/310224200866619719680000+- params:+    n: '23'+  number: 1/216862434431944426122117120000*x^22 - 1/2571491317374835092357120000*x^21+    + 1/73471180496423859781632000*x^20 - 31/122451967494039766302720000*x^19 + 19/7250445443726038794240000*x^18+    - 251/18455679311302644203520000*x^17 + 2437/179128652139113899622400000*x^16+    + 85961/537385956417341698867200000*x^15 - 31/112482670103054254080000*x^14 -+    1360769/723825982113154125004800000*x^13 + 10904357/8184801490048742798131200000*x^12+    + 1869962999/106402419370633656375705600000*x^11 + 70346681/4836473607756075289804800000*x^10+    - 32667203/403039467313006274150400000*x^9 - 81217/419832778451048202240000*x^8+    + 5533739/17129177360802766651392000000*x^7 + 13708906129/25693766041204149977088000000*x^6+    + 8698892071/12204538869571971239116800000*x^5 + 1029732337/9589280540377977402163200000*x^4+    - 132947/254362971638071296000000*x^3 - 269839961/582681977279911821312000000*x^2+    - 77683/620448401733239439360000*x+- params:+    n: '24'+  number: 1/10409396852733332453861621760000*x^23 - 1/113145617964492744063713280000*x^22+    + 1/2938847219856954391265280000*x^21 - 233/33062031223390736901734400000*x^20+    + 1/12052688529830298255360000*x^19 - 503/974459867636779613945856000*x^18 + 2117/2149543825669366795468800000*x^17+    + 2983/537385956417341698867200000*x^16 - 5233/264559240082383605596160000*x^15+    - 30454883/425609677482534625502822400000*x^14 + 12270233/65478411920389942385049600000*x^13+    + 27827329/30400691248752473250201600000*x^12 - 275267/723586700796753082318848000*x^11+    - 164796869/23215073317229161391063040000*x^10 - 3192584459/348226099758437420865945600000*x^9+    + 14913396679/822200513318532799266816000000*x^8 + 152506913641/2466601539955598397800448000000*x^7+    + 166493270833/3905452438263030796517376000000*x^6 - 124647957701681/1933198956940200244276101120000000*x^5+    - 4363941670597/32219982615670004071268352000000*x^4 - 2697566659399/33830981746453504274831769600000*x^3+    + 576654122683/108071191690059805322379264000000*x^2 + 19311547193251/878078432481735918244331520000000*x+    + 236364091/40651779281561848066867200000+- params:+    n: '25'+  number: 1/520469842636666622693081088000000*x^24 - 1/5204698426366666226930810880000*x^23+    + 1/123431583233992084433141760000*x^22 - 43/231434218563735158312140800000*x^21+    + 29/11755388879427817565061120000*x^20 - 257/14242105757768317434593280000*x^19+    + 3727/73084490072758471045939200000*x^18 + 443/2810941925875325809459200000*x^17+    - 757/721525200224682560716800000*x^16 - 1687193/851219354965069251005644800000*x^15+    + 22522321/1702438709930138502011289600000*x^14 + 58725649/1659877742181885039461007360000*x^13+    - 2707316981/30643896778742493036203212800000*x^12 - 22663379/52115470712147097000345600000*x^11+    - 59924939/696452199516874841731891200000*x^10 + 136265093773/57554035932297295948677120000000*x^9+    + 151497696367/34532421559378377569206272000000*x^8 - 223281317659/164029002407047293453729792000000*x^7+    - 53916176103281/3866397913880400488552202240000000*x^6 - 411768291581/24784602012053849285591040000000*x^5+    - 25405683763/19900577497913826044018688000000*x^4 + 149043299257/11375914914743137402355712000000*x^3+    + 19311547193251/1756156864963471836488663040000000*x^2 + 236364091/81303558563123696133734400000*x