A375671 Expansion of e.g.f. 1 / (1 + x * log(1 - x))^2.

1, 0, 4, 6, 88, 420, 5148, 44520, 587424, 7203168, 109106640, 1689621120, 29620245312, 546547098240, 10989238893696, 233884517368320, 5324618721070080, 128058198711690240, 3260308438558826496, 87336328336058603520, 2459915920512955929600

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A052830, A375672.

Cf. A052801, A375660.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x))^2))

PARI

a(n) = n!*sum(k=0, n\2, (k+1)!*abs(stirling(n-k, k, 1))/(n-k)!);

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052830.

a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)! * |Stirling1(n-k,k)|/(n-k)!.