%I #9 Jan 29 2024 09:00:09
%S 1,4,10,20,36,72,220,936,4045,15836,56174,187148,616651,2114448,
%T 7717752,29498000,114243269,437915876,1650264874,6149423732,
%U 22909545269,86129798600,327872238092,1260466647944,4867739842821,18801022899756,72501445905366
%N G.f. satisfies A(x) = 1/(1-x)^4 + x^4*A(x)^4.
%F a(n) = Sum_{k=0..floor(n/4)} binomial(n+8*k+3,n-4*k) * binomial(4*k,k) / (3*k+1).
%o (PARI) a(n) = sum(k=0, n\4, binomial(n+8*k+3, n-4*k)*binomial(4*k, k)/(3*k+1));
%Y Cf. A086615, A369691.
%Y Cf. A364591.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 29 2024