A380047 E.g.f. A(x) satisfies A(x) = 1 + 3*x*exp(x)*A(x)^(1/3).

1, 3, 12, 45, 132, 135, -702, 6573, 111576, -634581, -19482690, 104641713, 5438689380, -21226768017, -2173847986086, 3249084663765, 1168505502268848, 2167390942251219, -807540016560944778, -5035872168333504807, 693302551375611396540, 8209523136574257223383

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A380051.

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

Prog

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

Crossrefs

Cf. A006153, A380046.

Cf. A380051.

Sequence in context: A260146 A229936 A258626 * A064017 A005320 A062561

Adjacent sequences: A380044 A380045 A380046 * A380048 A380050 A380051

Keyword

sign

Author

Seiichi Manyama, Jan 11 2025

Status

approved