The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #8 Apr 11 2024 10:10:14
%S 1,2,4,24,112,688,4032,25856,165888,1103616,7412480,50699776,
%T 350087168,2444208128,17198686208,121945948160,870026493952,
%U 6242802761728,45016506564608,326071359897600,2371312632397824,17307835567636480,126743329792327680
%N G.f. A(x) satisfies A(x) = 1 + x/A(x) * (1 + A(x)^4).
%F a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(2*n-4*k-2,n-1) for n > 0.
%o (PARI) a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(2*n-4*k-2, n-1))/n);
%Y Cf. A112478, A348957, A364394, A364395, A366363.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 11 2024