%I #23 Dec 26 2024 03:02:06
%S 1,4,64,1424,36800,1036160,30843648,954671360,30415326208,
%T 990831196160,32853724512256,1105132250898432,37620337933582336,
%U 1293586791397064704,44863864476704768000,1567543145774827241472,55125711913212153954304
%N G.f. satisfies A(x) = 1 + x * A(x)^3 * (1 + A(x))^2.
%H Seiichi Manyama, <a href="/A371661/b371661.txt">Table of n, a(n) for n = 0..633</a>
%F a(n) = (1/n) * Sum_{k=0..floor((n-1)/2)} 4^(n-k) * binomial(n,k) * binomial(4*n-k,n-1-2*k) for n > 0.
%F a(n) = 2^n * A371669(n). - _Seiichi Manyama_, Dec 26 2024
%o (PARI) a(n) = if(n==0, 1, sum(k=0, (n-1)\2, 4^(n-k)*binomial(n, k)*binomial(4*n-k, n-1-2*k))/n);
%Y Cf. A271469, A363311, A371660.
%Y Cf. A371669.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 01 2024