cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A373855 a(n) = Sum_{k=1..n} k! * k^(n-1) * |Stirling1(n,k)|.

Original entry on oeis.org

0, 1, 5, 80, 2690, 155074, 13658386, 1706098008, 286888266696, 62485391828448, 17112247116585744, 5755236604915060944, 2331975856351260982848, 1120439648590390138640304, 629855675998212293917375344, 409557081242059531918330384896
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2024

Keywords

Crossrefs

Programs

  • Mathematica
    nmax=15; Range[0,nmax]!CoefficientList[Series[Sum[(-Log[1 - k*x])^k / k,{k,nmax}],{x,0,nmax}],x] (* Stefano Spezia, Jun 19 2024 *)
  • PARI
    a(n) = sum(k=1, n, k!*k^(n-1)*abs(stirling(n, k, 1)));

Formula

E.g.f.: Sum_{k>=1} (-log(1 - k*x))^k / k.

A373858 a(n) = Sum_{k=1..n} k! * k^(2*n-1) * Stirling1(n,k).

Original entry on oeis.org

0, 1, 15, 1268, 317294, 175542694, 181641609214, 315309390376056, 850661260866748728, 3370191684116333977872, 18768704088141613880906736, 141902519646656406912522712848, 1415862822521619228707500717132224, 18210234893009450819658863637633454608
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2024

Keywords

Crossrefs

Programs

  • Mathematica
    nmax=13; Range[0,nmax]!CoefficientList[Series[Sum[(Log[1 + k^2*x])^k / k,{k,nmax}],{x,0,nmax}],x] (* Stefano Spezia, Jun 19 2024 *)
  • PARI
    a(n) = sum(k=1, n, k!*k^(2*n-1)*stirling(n, k, 1));

Formula

E.g.f.: Sum_{k>=1} log(1 + k^2*x)^k / k.

A373861 a(n) = Sum_{k=0..n} k^(2*n) * |Stirling1(n,k)|.

Original entry on oeis.org

1, 1, 17, 923, 107724, 22369324, 7385651720, 3597082257152, 2449105468081600, 2238708422118782376, 2661994302285967390224, 4014423110086784061347592, 7519716937006429200213786240, 17194081369411703462470895338272
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2024

Keywords

Crossrefs

Programs

  • Mathematica
    Unprotect[Power]; Power[0, 0] = 1; Protect[Power]; nmax=13; Range[0,nmax]!CoefficientList[Series[Sum[(-Log[1 - k^2*x])^k / k!,{k,0,nmax}],{x,0,nmax}],x] (* Stefano Spezia, Jun 19 2024 *)
  • PARI
    a(n) = sum(k=0, n, k^(2*n)*abs(stirling(n, k, 1)));

Formula

E.g.f.: Sum_{k>=0} (-log(1 - k^2*x))^k / k!.
Showing 1-3 of 3 results.