A375662 Expansion of e.g.f. 1 / (1 - x^2 * (exp(x) - 1))^2.

1, 0, 0, 12, 24, 40, 2220, 15204, 70672, 1723824, 22710420, 202577980, 3841065624, 71221859592, 994632663388, 19005155049300, 421055077585440, 8033764197776224, 172109549363348772, 4285658639255113836, 101794836650015825320, 2516190299149752959160

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A358013, A375663.

Programs

PARI

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

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A358013.

a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)! * Stirling2(n-2*k,k)/(n-2*k)!.