A377964 - OEIS

%I #10 Nov 13 2024 06:47:25

%S 1,2,9,58,389,3186,29437,294554,3233673,38350594,484794641,6522118362,

%T 92857444429,1390937221298,21858658599429,359271578140666,

%U 6156249977141777,109722278546645634,2029772196329985433,38893956306343711994,770622936760496106261,15763542538016019828082

%N Expansion of e.g.f. (1+x) * exp(x*(1+x)^3).

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

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

%Y Cf. A018191, A377963.

%Y Cf. A361279, A377966, A377967.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Nov 12 2024