A375808 Expansion of e.g.f. 1/(1 + (log(1 - x^3))/x^2)^2.

1, 2, 6, 24, 144, 1080, 9360, 94080, 1078560, 13789440, 194745600, 3013718400, 50654419200, 918900702720, 17896250211840, 372338481715200, 8241399758592000, 193366506222489600, 4793430516921446400, 125181207625240166400, 3435031723216084992000

Offset: 0

Author

Seiichi Manyama, Aug 29 2024

Keywords

• nonn

Crossrefs

Cf. A375799, A375809.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^3)/x^2)^2))

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375799.

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