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.

A384136 a(n) = (3*n)!/(2*n)! * Sum_{k=1..n} 1/(2*n+k).

Original entry on oeis.org

1, 11, 191, 4578, 140274, 5238132, 230784840, 11720201616, 674092013040, 43310839531680, 3074579815271040, 238983481496188800, 20187063842072319360, 1841332369689189619200, 180372122189263722009600, 18885338733119777188300800, 2104722524872544008142592000
Offset: 1

Views

Author

Seiichi Manyama, May 20 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, k*(2*n+1)^(k-1)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} k * (2*n+1)^(k-1) * |Stirling1(n,k)|.
a(n) = n! * [x^n] (-log(1 - x)/(1 - x)^(2*n+1)).

A384171 a(n) = 2^n * n! * binomial(5*n/2,n) * Sum_{k=1..n} 1/(3*n+2*k).

Original entry on oeis.org

1, 18, 503, 19312, 946009, 56419200, 3967700295, 321506211840, 29497821190065, 3022798062551040, 342204383046633975, 42414460290839347200, 5712600791700063700425, 830773593435129407078400, 129744737403826992957167175, 21657021896289762215460864000, 3847769544999445159548440534625
Offset: 1

Views

Author

Seiichi Manyama, May 21 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, k*(3*n+2)^(k-1)*2^(n-k)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} k * (3*n+2)^(k-1) * 2^(n-k) * |Stirling1(n,k)|.
a(n) = n! * [x^n] ( -log(1 - 2*x)/(2 * (1 - 2*x)^(3*n/2+1)) ).

A384172 a(n) = 4^n * n! * binomial(7*n/4,n) * Sum_{k=1..n} 1/(3*n+4*k).

Original entry on oeis.org

1, 24, 851, 40832, 2483269, 183241728, 15912395295, 1590131687424, 179766351690345, 22685041361848320, 3161081216499580395, 482101740659382681600, 79876921394710650447405, 14287114673531430042009600, 2743817201103924825303993975, 563131793021994402478188134400
Offset: 1

Views

Author

Seiichi Manyama, May 21 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, k*(3*n+4)^(k-1)*4^(n-k)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} k * (3*n+4)^(k-1) * 4^(n-k) * |Stirling1(n,k)|.
a(n) = n! * [x^n] ( -log(1 - 4*x)/(4 * (1 - 4*x)^(3*n/4+1)) ).
Showing 1-3 of 3 results.