This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A364331 #23 Mar 27 2025 23:27:45
%S A364331 1,2,15,163,2070,28698,421015,6425644,100977137,1622885389,
%T A364331 26551709946,440744175801,7404449354076,125657625548824,
%U A364331 2150963575012295,37094953102567208,643904274979347286,11241232087809137759,197247501440314516840,3476787208220672891388,61533794803235280779261
%N A364331 G.f. satisfies A(x) = (1 + x*A(x)^2) * (1 + x*A(x)^5).
%F A364331 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).
%F A364331 x/series_reversion(x*A(x)) = 1 + 2*x + 11*x^2 + 89*x^3 + 836*x^4 + ..., the g.f. of A215623. - _Peter Bala_, Sep 08 2024
%p A364331 A364331 := proc(n)
%p A364331 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 A364331 end proc:
%p A364331 seq(A364331(n),n=0..70); # _R. J. Mathar_, Jul 25 2023
%o A364331 (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 A364331 Cf. A007863, A069271, A073157, A215654, A215715, A364333.
%Y A364331 Cf. A215623, A215624, A239108, A364335, A364338.
%Y A364331 Cf. A200719.
%K A364331 nonn,easy
%O A364331 0,2
%A A364331 _Seiichi Manyama_, Jul 18 2023