%I #8 Jul 30 2023 09:56:32
%S 1,3,7,22,97,469,2339,12148,65295,358979,2006977,11380702,65311575,
%T 378574425,2213092750,13032826536,77244242937,460413902079,
%U 2758088752351,16596379614234,100269075879881,607996092039949,3698873710967989,22570809986322440
%N G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^4.
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n+7*k+2,9*k+2) * binomial(4*k,k) / (3*k+1).
%o (PARI) a(n) = sum(k=0, n\2, binomial(n+7*k+2, 9*k+2)*binomial(4*k, k)/(3*k+1));
%Y Cf. A364625, A364626.
%Y Cf. A364622.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jul 30 2023