A377689 E.g.f. satisfies A(x) = (1 + x * (exp(x*A(x)) - 1))^3.

1, 0, 6, 9, 300, 1995, 48438, 720111, 17965944, 422161011, 12234150930, 380328463383, 13151800946628, 497667965729259, 20320277028840558, 899482574279597535, 42525760204244934768, 2153233176660303831267, 115738033009558749725610, 6600044862098481204272487

Offset: 0

Author

Seiichi Manyama, Nov 04 2024

Keywords

• nonn

Crossrefs

Cf. A371115, A377688.

Cf. A377690.

Programs

PARI

a(n) = 3*n!*sum(k=0, n\2, (3*n-3*k+2)!*stirling(n-k, k, 2)/((n-k)!*(3*n-4*k+3)!));

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377690.

a(n) = 3 * n! * Sum_{k=0..floor(n/2)} (3*n-3*k+2)! * Stirling2(n-k,k)/( (n-k)! * (3*n-4*k+3)! ).