%I #9 Aug 25 2023 09:43:57
%S 1,1,6,46,411,3996,41062,438662,4823133,54221518,620404859,7201317005,
%T 84590041441,1003656037278,12010861830069,144804336388912,
%U 1757106190680819,21443109365898743,263009775111233392,3240530659303505547,40088688455992604594
%N G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)).
%F a(n) = Sum_{k=0..n} binomial(n+4*k+1,k) * binomial(k,n-k)/(n+4*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(k, n-k)/(n+4*k+1));
%Y Cf. A002295, A365184, A365186, A365187, A365188, A365189.
%Y Cf. A364748.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 25 2023
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