A363479 - OEIS

%I #13 Aug 17 2023 08:16:16

%S 1,1,9,160,4381,162816,7663669,437164288,29317265625,2260685099008,

%T 197088986941921,19170218777296896,2058199476739788661,

%U 241779221463040000000,30847476924400409437389,4247859315849037948911616,627960846411135123552180529

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

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

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

%Y Cf. A088695, A363358.

%Y Cf. A361094.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 17 2023