A377720 E.g.f. satisfies A(x) = (1 + x * (exp(x) - 1) * A(x))^3.

1, 0, 6, 9, 300, 1455, 44658, 430941, 13821048, 213210171, 7400153550, 160981385433, 6126989357844, 173482562393751, 7273217782923498, 253885773923800245, 11726322434886352368, 485729504795911017075, 24658741688798553168582, 1179026561203600147075857

Offset: 0

Author

Seiichi Manyama, Nov 04 2024

Keywords

• nonn

Crossrefs

Cf. A371143, A377691.

Programs

PARI

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A371143.

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