A380045 E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x)*A(x) )^(1/3).

1, 1, 8, 109, 2220, 60585, 2079166, 86098929, 4179685560, 232849349425, 14645304783450, 1026614846280441, 79371261554884036, 6709919722961129337, 615776691767279304822, 60968162469515187248545, 6478143744223567852425456, 735290556968263062361451745, 88790542940636437330983140146

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n! * Sum_{k=0..n} 3^k * k^(n-k) * binomial(4*k/3+1/3,k)/( (4*k+1)*(n-k)! ).

Prog

(PARI) a(n) = n!*sum(k=0, n, 3^k*k^(n-k)*binomial(4*k/3+1/3, k)/((4*k+1)*(n-k)!));

Crossrefs

Cf. A295238, A380044.

Sequence in context: A322718 A309188 A371385 * A098623 A297971 A076151

Adjacent sequences: A380042 A380043 A380044 * A380046 A380047 A380048

Keyword

nonn

Author

Seiichi Manyama, Jan 10 2025

Status

approved