A375558 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, 1961530116170625000, 1606200062942475000

Offset: 0

Author

Seiichi Manyama, Aug 19 2024

Keywords

• nonn

Crossrefs

Cf. A052830, A375167, A375556.

Programs

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)!*abs(stirling(k, n-4*k, 1))/(24^k*k!));

Formula

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