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%I #16 Jul 25 2023 08:16:39
%S 1,2,15,163,2070,28698,421015,6425644,100977137,1622885389,
%T 26551709946,440744175801,7404449354076,125657625548824,
%U 2150963575012295,37094953102567208,643904274979347286,11241232087809137759,197247501440314516840,3476787208220672891388,61533794803235280779261
%N G.f. satisfies A(x) = (1 + x*A(x)^2) * (1 + x*A(x)^5).
%F a(n) = Sum_{k=0..n} binomial(2*n+3*k+1,k) * binomial(2*n+3*k+1,n-k) / (2*n+3*k+1).
%p A364331 := proc(n)
%p add( binomial(2*n+3*k+1,k) * binomial(2*n+3*k+1,n-k)/(2*n+3*k+1),k=0..n) ;
%p end proc:
%p seq(A364331(n),n=0..70); # _R. J. Mathar_, Jul 25 2023
%o (PARI) a(n) = sum(k=0, n, binomial(2*n+3*k+1, k)*binomial(2*n+3*k+1, n-k)/(2*n+3*k+1));
%Y Cf. A007863, A069271, A073157, A215654, A215715, A364333.
%Y Cf. A215624, A239108, A364335, A364338.
%Y Cf. A200719.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jul 18 2023
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