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.

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).

A380370 Expansion of e.g.f. log( 1 - log(1 - x)^5 / 120 ).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 15, 175, 1960, 22449, 269199, 3410000, 45753180, 650179816, 9771920158, 155020511282, 2589903552600, 45462951235584, 836599468436514, 16102788580144350, 323508284210923974, 6770014833358706076, 147290030512050486060, 3325319844639779998836
Offset: 0

Views

Author

Seiichi Manyama, Jan 23 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n\5, (-1)^(k-1)*(5*k)!*abs(stirling(n, 5*k, 1))/(k*120^k));

Formula

a(n) = Sum_{k=1..floor(n/5)} (-1)^(k-1) * (5*k)! * |Stirling1(n,5*k)|/(k * 120^k).
a(n) = |Stirling1(n,5)| - Sum_{k=1..n-1} |Stirling1(k,5)| * binomial(n-1,k) * a(n-k).
Showing 1-3 of 3 results.