A375561 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2)).

1, 0, 0, 6, 0, 60, 720, 1680, 40320, 453600, 3326400, 67858560, 878169600, 11935123200, 240708948480, 3946374432000, 73927190937600, 1621341859737600, 32960791774310400, 758085507686707200, 18570669277095936000, 454016684061997056000, 12100759898595611443200

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) ~ n! * r^(n+1) * (r^2 - 1) / (2 - r + r^3), where r = 1.197019671936488528937062183033935713041032105791232... is the root of the equation 1 - exp(-r) = 1/r^2. - Vaclav Kotesovec, Sep 30 2025

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, (n-2*k)!*abs(stirling(k, n-2*k, 1))/k!);

Crossrefs

Cf. A052830, A375562.

Cf. A353226.

Sequence in context: A353226 A191688 A375588 * A375831 A375830 A375833

Adjacent sequences: A375558 A375559 A375560 * A375562 A375563 A375564

Keyword

nonn

Author

Seiichi Manyama, Aug 19 2024

Status

approved