A375697 Expansion of e.g.f. 1 / (1 - 3 * x * (exp(x) - 1))^(2/3).

1, 0, 4, 6, 128, 610, 11712, 107114, 2167776, 30285378, 678296720, 12761459722, 321364284144, 7550564959106, 214210299545088, 5993932335381930, 190756625697021632, 6161493279498219394, 218469987108304908336, 7972839360644407925258

Offset: 0

Author

Seiichi Manyama, Aug 24 2024

Keywords

• nonn

Crossrefs

Cf. A367881, A375696.

Cf. A375689.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*(exp(x)-1))^(2/3)))

PARI

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

Formula

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