A375685 Expansion of e.g.f. 1 / (1 + x^2/2 * log(1 - x))^2.

1, 0, 0, 6, 12, 40, 720, 4788, 34440, 460080, 5246640, 60318720, 879523920, 13298126400, 206628117696, 3575354428800, 65828785276800, 1264510188264960, 25912058505776640, 561351949518931200, 12721171715573529600, 302794615563937781760, 7554095183751745305600

Offset: 0

Author

Seiichi Manyama, Aug 24 2024

Keywords

• nonn

Crossrefs

Cf. A351505, A375686.

Cf. A375237.

Programs

PARI

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

PARI

a(n) = n!*sum(k=0, n\3, (k+1)!*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A351505.

a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)! * |Stirling1(n-2*k,k)|/(2^k*(n-2*k)!).