A375560 Expansion of e.g.f. 1 / (1 - x * log(1 + x^4/24)).

1, 0, 0, 0, 0, 5, 0, 0, 0, -315, 6300, 0, 0, 150150, -6306300, 94594500, 0, -268017750, 17689171500, -549972423000, 7332965640000, 1283268987000, -117632990475000, 5681673439942500, -155840185781280000, 1934474528361375000, 1606200062942475000

Offset

0,6

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (n-4*k)! * Stirling1(k,n-4*k)/(24^k*k!).

Mathematica

With[{nn=30}, CoefficientList[Series[1/(1-x Log[1+x^4/24]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 21 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*log(1+x^4/24))))
(PARI) a(n) = n!*sum(k=0, n\4, (n-4*k)!*stirling(k, n-4*k, 1)/(24^k*k!));

Crossrefs

Cf. A375557.

Sequence in context: A380284 A047754 A048682 * A375558 A186716 A331039

Adjacent sequences: A375557 A375558 A375559 * A375561 A375562 A375563

Keyword

sign

Author

Seiichi Manyama, Aug 19 2024

Status

approved