A365033 - OEIS

%I #10 Aug 18 2023 08:26:47

%S 1,1,9,127,2769,80861,2976733,132394011,6909143265,414041227417,

%T 28025981914581,2115049310887679,176095675272002929,

%U 16035108243371426613,1585349332849711046829,169128107565128349122851,19365426435579375683158977,2368882573995841615546652081

%N E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x))^2).

%F a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(2*k,n-k)/k!.

%o (PARI) a(n) = n!*sum(k=0, n, (n+k+1)^(k-1)*binomial(2*k, n-k)/k!);

%Y Cf. A363357, A365034.

%Y Cf. A364941.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 17 2023