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.

A367158 E.g.f. satisfies A(x) = 1 - A(x)^3 * log(1 - x).

Original entry on oeis.org

1, 1, 7, 92, 1824, 48804, 1649724, 67492872, 3243567552, 179139978072, 11181615816216, 778466939121552, 59811143359463952, 5027200928936108064, 458865351655379262432, 45201262487568977507328, 4779609140451030860102400, 539990133396500652971120640
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2023

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Sum[(-1)^(n-k) * (3*k)!/(2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)
  • PARI
    a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} (3*k)!/(2*k+1)! * |Stirling1(n,k)|.
a(n) ~ 9 * n^(n-1) / (2^(5/2) * exp(23*n/27) * (exp(4/27) - 1)^(n - 1/2)). - Vaclav Kotesovec, Nov 10 2023

A367161 E.g.f. satisfies A(x) = 1 + A(x)^3 * (exp(x) - 1).

Original entry on oeis.org

1, 1, 7, 91, 1795, 47851, 1612027, 65731891, 3148530595, 173319612571, 10782796483147, 748237171338691, 57299882326956595, 4800323120225595691, 436719009263680421467, 42878536726317406241491, 4519124182661042439577795, 508885588456024192452993211
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2023

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Sum[(3*k)!/(2*k+1)! * StirlingS2[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)
  • PARI
    a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*stirling(n, k, 2));

Formula

a(n) = Sum_{k=0..n} (3*k)!/(2*k+1)! * Stirling2(n,k).
a(n) ~ sqrt(93) * n^(n-1) / (2^(5/2) * log(31/27)^(n - 1/2) * exp(n)). - Vaclav Kotesovec, Nov 10 2023

A367155 E.g.f. satisfies A(x) = 1 + A(x)^3 * log(1 + x).

Original entry on oeis.org

1, 1, 5, 56, 948, 21804, 634284, 22348584, 925322784, 44039346264, 2369167375656, 142173632632272, 9416315321258928, 682290228636729504, 53689645309437175968, 4559660591348115191808, 415683140400707316145920, 40490500091575002629253120
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2023

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Sum[(3*k)!/(2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)
  • PARI
    a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*stirling(n, k, 1));

Formula

a(n) = Sum_{k=0..n} (3*k)!/(2*k+1)! * Stirling1(n,k).
a(n) ~ 9 * n^(n-1) / (2^(5/2) * (exp(4/27) - 1)^(n - 1/2) * exp(n + 2/27)). - Vaclav Kotesovec, Nov 10 2023
Showing 1-3 of 3 results.