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%I #9 Aug 25 2023 09:44:01
%S 1,1,6,47,428,4241,44407,483358,5414618,62014112,722870120,8547768832,
%T 102284029963,1236274747490,15070955944288,185089043535730,
%U 2287843817573898,28440852786725695,355345599519983962,4459821165693379625,56200963128262312342
%N G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^2).
%F a(n) = Sum_{k=0..n} binomial(2*n+3*k+1,k) * binomial(k,n-k)/(2*n+3*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(2*n+3*k+1, k)*binomial(k, n-k)/(2*n+3*k+1));
%Y Cf. A002295, A365184, A365185, A365187, A365188, A365189.
%Y Cf. A365192.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 25 2023
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