A375696 Expansion of e.g.f. 1 / (1 - 3 * x * (exp(x) - 1))^(1/3).

1, 0, 2, 3, 52, 245, 4206, 37807, 712552, 9755433, 207915490, 3830073731, 92948571420, 2139142283005, 58945940093782, 1617324856023255, 50252559901690576, 1593701025177559121, 55366628370374688714, 1986560560083994301611

Offset: 0

Author

Seiichi Manyama, Aug 24 2024

Keywords

• nonn

Crossrefs

Cf. A367881, A375697.

Cf. A375688.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*(exp(x)-1))^(1/3)))

PARI

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

Formula

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