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 1-2 of 2 results.

A377376 Expansion of e.g.f. log( 1 - log(1 - x)^3 / 6 ).

Original entry on oeis.org

0, 0, 0, 1, 6, 35, 215, 1414, 9912, 73324, 565170, 4472226, 35725426, 283350132, 2225790476, 18624038224, 216679183120, 4293834561200, 111300845967440, 2963219043255360, 76258914698507280, 1895550595605889760, 45928558583373219600, 1093984400513512753840
Offset: 0

Views

Author

Seiichi Manyama, Jan 23 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n\3, (-1)^(k-1)*(3*k)!*abs(stirling(n, 3*k, 1))/(k*6^k));

Formula

a(n) = Sum_{k=1..floor(n/3)} (-1)^(k-1) * (3*k)! * |Stirling1(n,3*k)|/(k * 6^k).
a(n) = |Stirling1(n,3)| - Sum_{k=1..n-1} |Stirling1(k,3)| * binomial(n-1,k) * a(n-k).

A379674 Expansion of e.g.f. -log( 1 - log(1 - x)^4 / 24 ).

Original entry on oeis.org

0, 0, 0, 0, 1, 10, 85, 735, 6804, 68544, 754130, 9044750, 117779431, 1657347978, 25083122701, 406495546275, 7025691638029, 129034238530984, 2510053743368448, 51563288466007704, 1115617292385725186, 25359995212317017700, 604332959567317283050, 15066452630930326289950
Offset: 0

Views

Author

Seiichi Manyama, Jan 23 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n\4, (4*k)!*abs(stirling(n, 4*k, 1))/(k*24^k));

Formula

a(n) = Sum_{k=1..floor(n/4)} (4*k)! * |Stirling1(n,4*k)|/(k * 24^k).
a(n) = |Stirling1(n,4)| + Sum_{k=1..n-1} |Stirling1(k,4)| * binomial(n-1,k) * a(n-k).
Showing 1-2 of 2 results.