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.

A357904 a(n) = Sum_{k=0..floor(n/4)} Stirling2(n - 3*k,k).

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 1, 1, 2, 4, 8, 16, 33, 70, 153, 346, 814, 2000, 5138, 13776, 38395, 110695, 328638, 1001306, 3124626, 9978906, 32620854, 109225582, 374875483, 1319392590, 4761630252, 17610041358, 66668257846, 258018795970, 1019440760020, 4106982942054
Offset: 0

Views

Author

Seiichi Manyama, Oct 19 2022

Keywords

Crossrefs

Cf. A000110, A171367, A357903.

Programs

  • PARI
    a(n) = sum(k=0, n\4, stirling(n-3*k, k, 2));
  • PARI
    my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(4*k)/prod(j=1, k, 1-j*x)))

Formula

G.f.: Sum_{k>=0} x^(4*k)/Product_{j=1..k} (1 - j * x).

A357925 a(n) = Sum_{k=0..floor(n/3)} Stirling2(n - 2*k,n - 3*k).

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 7, 12, 23, 47, 95, 192, 402, 869, 1898, 4181, 9379, 21431, 49556, 115770, 273919, 656476, 1590061, 3888783, 9608337, 23980678, 60402964, 153469477, 393325442, 1016628823, 2648842279, 6955029849, 18400676786, 49042936328, 131646082259
Offset: 0

Views

Author

Seiichi Manyama, Oct 20 2022

Keywords

Crossrefs

Cf. A024428, A357926.
Cf. A357903.

Programs

  • Mathematica
    Table[Sum[StirlingS2[n-2k,n-3k],{k,0,Floor[n/3]}],{n,0,40}] (* Harvey P. Dale, Feb 22 2024 *)
  • PARI
    a(n) = sum(k=0, n\3, stirling(n-2*k, n-3*k, 2));
  • PARI
    my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/prod(j=1, k, 1-j*x^3)))

Formula

G.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - j * x^3).

A357939 a(n) = Sum_{k=0..floor(n/2)} Stirling2(k,n - 2*k).

Original entry on oeis.org

1, 0, 0, 1, 0, 1, 1, 1, 3, 2, 7, 7, 16, 26, 41, 92, 128, 317, 478, 1107, 1977, 4077, 8547, 16310, 37775, 71489, 170660, 339138, 795833, 1705058, 3876254, 8926023, 19888522, 48187837, 107726407, 267597455, 613509355, 1531527270, 3646775589, 9066267823
Offset: 0

Views

Author

Seiichi Manyama, Oct 21 2022

Keywords

Crossrefs

Cf. A357940, A357941.
Cf. A357903.

Programs

  • Mathematica
    Table[Sum[StirlingS2[k,n-2k],{k,0,Floor[n/2]}],{n,0,40}] (* Harvey P. Dale, Jul 22 2025 *)
  • PARI
    a(n) = sum(k=0, n\2, stirling(k, n-2*k, 2));
  • PARI
    my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k)/prod(j=1, k, 1-j*x^2)))

Formula

G.f.: Sum_{k>=0} x^(3*k)/Product_{j=1..k} (1 - j * x^2).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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