A379940 E.g.f. A(x) satisfies A(x) = 1/( exp(-x*A(x)^(2/3)) - x*A(x)^(1/3) )^3.

1, 6, 81, 1788, 55785, 2267298, 114015825, 6848257272, 478929874257, 38253577287870, 3437561332041969, 343381977748134900, 37755068758105209849, 4531920849132497127258, 589779214651388664049905, 82722149483353129407482352, 12440903535778778244423710625, 1997259670949248788135594940278

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377892.

a(n) = 3 * n! * Sum_{k=0..n} (2*n+3)^(k-1) * binomial(2*n+3,n-k)/k!.

a(n) == 0 (mod 3) for n>0.

Prog

(PARI) a(n) = 3*n!*sum(k=0, n, (2*n+3)^(k-1)*binomial(2*n+3, n-k)/k!);

Crossrefs

Cf. A377892, A379936.

Sequence in context: A349505 A052756 A349651 * A193265 A317277 A138457

Adjacent sequences: A379937 A379938 A379939 * A379941 A379942 A379943

Keyword

nonn,new

Author

Seiichi Manyama, Jan 07 2025

Status

approved