%I #10 Oct 15 2023 09:26:05
%S 1,0,0,0,1,4,10,20,39,88,228,600,1507,3652,8866,22100,56365,144656,
%T 369784,942480,2408934,6196280,16026652,41571640,107959654,280708560,
%U 731349400,1910098320,4999759830,13109582376,34421585844,90500370760,238272324682
%N G.f. A(x) satisfies A(x) = 1 + (x * A(x) / (1 - x))^4.
%F a(n) = Sum_{k=0..floor(n/4)} binomial(n-1,n-4*k) * binomial(4*k,k) / (3*k+1).
%o (PARI) a(n) = sum(k=0, n\4, binomial(n-1, n-4*k)*binomial(4*k, k)/(3*k+1));
%Y Partial sums give A127902.
%Y Cf. A213336, A364410, A366645.
%Y Cf. A002026, A361932.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Oct 15 2023