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

0,3

Links

Table of n, a(n) for n=0..20.

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)!.

a(n) ~ sqrt(2*Pi) * r^n * n^(n + 3/2) / ((1 + 1/(r*(r-1)))^2 * exp(n)), where r = 1.34997648540112544262746690676132084912056729543... is the root of the equation (r-1)*exp(r) = r. - Vaclav Kotesovec, Jan 23 2026

Prog

(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)!);

Crossrefs

Cf. A052830, A375672.

Cf. A052801, A375660.

Sequence in context: A101138 A222483 A245011 * A012897 A013079 A222495

Adjacent sequences: A375668 A375669 A375670 * A375672 A375673 A375674

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2024

Status

approved