A377741 - OEIS

%I #11 Nov 06 2024 04:37:22

%S 1,4,37,583,13225,394681,14659537,652829857,33937422001,2018665692721,

%T 135274646371561,10087017309339433,828563190097478425,

%U 74348364577760978329,7236649495742795579809,759466703902106082652321,85492204279344776678878945,10275933748282019792253453025

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

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

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

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

%Y Cf. A072597, A377740.

%Y Cf. A364983, A377575.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 05 2024