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.

A373869 a(n) = Sum_{k=1..n} k! * k^(n-3) * Stirling1(n,k).

Original entry on oeis.org

0, 1, 0, 2, 26, 674, 28894, 1848216, 165229560, 19698788448, 3022496261616, 580460752264656, 136441193196585408, 38540172064949405616, 12883204327833557091984, 5030833813902039858261504, 2269484487197629285690675584, 1171368942033975021150888242304
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, k!*k^(n-3)*stirling(n, k, 1));

Formula

E.g.f.: Sum_{k>=1} log(1 + k*x)^k / k^3.

A373873 a(n) = Sum_{k=1..n} k! * k^(n-2) * Stirling2(n,k).

Original entry on oeis.org

0, 1, 3, 31, 765, 34651, 2502213, 263824891, 38248036725, 7298877611371, 1773652375115973, 534749297993098651, 195883403209280580885, 85687658454617655817291, 44120264185381411695106533, 26413555571018242181844978811
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2024

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Sum[k! k^(n-2) StirlingS2[n,k],{k,n}],{n,0,20}] (* Harvey P. Dale, Jul 13 2025 *)
  • PARI
    a(n) = sum(k=1, n, k!*k^(n-2)*stirling(n, k, 2));

Formula

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

A373875 a(n) = Sum_{k=1..n} k! * k^(n-2) * |Stirling1(n,k)|.

Original entry on oeis.org

0, 1, 3, 32, 802, 36854, 2698598, 288450168, 42388536888, 8198703649296, 2019226648157472, 616991110153816848, 229048514514263311008, 101540936651344709359632, 52984383824921037875927760, 32145394332240602286960456192
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, k!*k^(n-2)*abs(stirling(n, k, 1)));

Formula

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