A367885 Expansion of e.g.f. 1/(1 - x * (exp(2*x) - 1)).

1, 0, 4, 12, 128, 1040, 12672, 161728, 2481152, 41806080, 791613440, 16399944704, 371591995392, 9110211874816, 240670782291968, 6810264853463040, 205583847590985728, 6593508525460226048, 223913466256013918208, 8026367531323488993280

Offset: 0

Author

Seiichi Manyama, Dec 04 2023

Keywords

• nonn

Crossrefs

Cf. A052848, A367886.

Cf. A337038, A351736.

Programs

PARI

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

Formula

a(0) = 1; a(n) = n * Sum_{k=2..n} 2^(k-1) * binomial(n-1,k-1) * a(n-k).

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