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.

A368174 Expansion of e.g.f. -log(1 - x^3/6 * (exp(x) - 1)).

Original entry on oeis.org

0, 0, 0, 0, 4, 10, 20, 35, 616, 5124, 29520, 138765, 1312300, 16576846, 175795984, 1539037955, 15687832720, 216382727240, 3170822906976, 42007311638169, 553841577209940, 8435274815148370, 145708900713412960, 2517047758252082671, 42575155321545439384
Offset: 0

Views

Author

Seiichi Manyama, Dec 14 2023

Keywords

Comments

This sequence is different from A354001.

Links

Crossrefs

Cf. A052858, A368173.
Cf. A353999, A354001.

Programs

  • PARI
    a(n) = n!*sum(k=1, n\4, (k-1)!*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));

Formula

a(n) = n! * Sum_{k=1..floor(n/4)} (k-1)! * Stirling2(n-3*k,k)/(6^k * (n-3*k)!).
a(0) = a(1) = a(2) = a(3) = 0; a(n) = binomial(n,3) + Sum_{k=4..n-1} binomial(k,3) * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Jan 22 2025

A366564 Expansion of e.g.f. -log(1 - x^2 * (exp(x) - 1)).

Original entry on oeis.org

0, 0, 0, 6, 12, 20, 390, 2562, 11816, 166392, 1970730, 17131070, 241009692, 3861669396, 51411143966, 828234487290, 15865154629200, 283329069136112, 5431892804244306, 119420738547382134, 2628980439169097540, 59707303735169923980, 1488953374718002643142
Offset: 0

Views

Author

Seiichi Manyama, Dec 15 2023

Keywords

Crossrefs

Cf. A052858, A366751.
Cf. A366459, A368173.

Programs

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

Formula

a(n) = n! * Sum_{k=1..floor(n/3)} (k-1)! * Stirling2(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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