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A364591 G.f. satisfies A(x) = 1/(1-x) + x^4*A(x)^4.

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%I A364591 #10 Jul 29 2023 10:54:05
%S A364591 1,1,1,1,2,5,11,21,40,85,197,457,1028,2289,5193,12069,28338,66445,
%T A364591 155563,365701,865815,2061133,4919431,11758741,28165412,67657225,
%U A364591 162977081,393445865,951438682,2304494349,5591221729,13588455861,33075115578,80616857525,196742749155
%N A364591 G.f. satisfies A(x) = 1/(1-x) + x^4*A(x)^4.
%F A364591 a(n) = Sum_{k=0..floor(n/4)} binomial(n-k,3*k) * binomial(4*k,k) / (3*k+1).
%o A364591 (PARI) a(n) = sum(k=0, n\4, binomial(n-k, 3*k)*binomial(4*k, k)/(3*k+1));
%Y A364591 Cf. A346073, A364590.
%Y A364591 Cf. A226974, A349289, A364588.
%K A364591 nonn,easy
%O A364591 0,5
%A A364591 _Seiichi Manyama_, Jul 29 2023