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.

A368166 Expansion of e.g.f. -log(1 + x^3/6 * log(1 - x)).

Original entry on oeis.org

0, 0, 0, 0, 4, 10, 40, 210, 1904, 15120, 132600, 1293600, 14673120, 178738560, 2341182480, 32915282400, 499117301760, 8075042976000, 138689356915200, 2519863488979200, 48354005826489600, 976893364144857600, 20721305503846886400, 460363370406207206400
Offset: 0

Views

Author

Seiichi Manyama, Dec 14 2023

Keywords

Comments

This sequence is different from A351493.

Links

Crossrefs

Cf. A052804, A368165.
Cf. A351493, A351506.

Programs

  • PARI
    a(n) = n!*sum(k=1, n\4, (k-1)!*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));

Formula

a(n) = n! * Sum_{k=1..floor(n/4)} (k-1)! * |Stirling1(n-3*k,k)|/(6^k * (n-3*k)!).
a(0) = a(1) = a(2) = a(3) = 0; a(n) = n!/(6*(n-3)) + Sum_{k=4..n-1} k!/(6*(k-3)) * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Jan 22 2025

A366752 Expansion of e.g.f. -log(1 + x^2 * log(1 - x)).

Original entry on oeis.org

0, 0, 0, 6, 12, 40, 540, 3528, 25200, 324000, 3648960, 41690880, 622274400, 9573033600, 150465579264, 2705877820800, 51819600268800, 1028013655818240, 22086154437442560, 504188626820659200, 11997041025160396800, 301999960230701322240
Offset: 0

Views

Author

Seiichi Manyama, Dec 15 2023

Keywords

Crossrefs

Cf. A052804, A366777.
Cf. A368165.

Programs

  • PARI
    a(n) = n!*sum(k=1, n\3, (k-1)!*abs(stirling(n-2*k, k, 1))/(n-2*k)!);

Formula

a(n) = n! * Sum_{k=1..floor(n/3)} (k-1)! * |Stirling1(n-2*k,k)|/(n-2*k)!.

A380339 Expansion of e.g.f. log(1 - x^2/2 * log(1 - x)).

Original entry on oeis.org

0, 0, 0, 3, 6, 20, 0, -126, -1260, 3240, 108360, 1635480, 15075720, 119957760, 705729024, 6324040800, 130989549600, 3572031415680, 78736127656320, 1502102645890560, 25514633892182400, 423898384988494080, 7590291773745542400, 162254912688831916800, 4023271392778314673920
Offset: 0

Views

Author

Seiichi Manyama, Jan 22 2025

Keywords

Crossrefs

Cf. A089064, A380338.
Cf. A368165, A368173.

Programs

  • PARI
    a(n) = n!*sum(k=1, n\3, (-1)^(k-1)*(k-1)!*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));

Formula

a(n) = n! * Sum_{k=1..floor(n/3)} (-1)^(k-1) * (k-1)! * |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).
a(0) = a(1) = a(2) = 0; a(n) = n!/(2*(n-2)) - Sum_{k=3..n-1} k!/(2*(k-2)) * binomial(n-1,k) * a(n-k).
Showing 1-3 of 3 results.

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

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