A377741 E.g.f. satisfies A(x) = exp(x) * (1 + x * A(x))^3.

1, 4, 37, 583, 13225, 394681, 14659537, 652829857, 33937422001, 2018665692721, 135274646371561, 10087017309339433, 828563190097478425, 74348364577760978329, 7236649495742795579809, 759466703902106082652321, 85492204279344776678878945, 10275933748282019792253453025

Offset

0,2

Links

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

Formula

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

a(n) = A364983(n+1)/(n+1).

Prog

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

Crossrefs

Cf. A072597, A377740.

Cf. A364983, A377575.

Sequence in context: A121080 A001518 A185082 * A259822 A345102 A036245

Adjacent sequences: A377738 A377739 A377740 * A377742 A377743 A377744

Keyword

nonn

Author

Seiichi Manyama, Nov 05 2024

Status

approved