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 A372090 #8 Apr 18 2024 09:29:02
%S A372090 1,2,12,88,728,6464,60192,579968,5733728,57834496,592831616,
%T A372090 6157627392,64667721472,685526908928,7325711938560,78832088481792,
%U A372090 853511147742720,9290927259254784,101623578654689280,1116343335709048832,12310726500144599040
%N A372090 G.f. A(x) satisfies A(x) = 1/( 1 - 4*x*A(x)*(1 + x*A(x)) )^(1/2).
%F A372090 a(n) = (1/(n+1)) * Sum_{k=0..n} 4^k * binomial(n/2+k-1/2,k) * binomial(k,n-k).
%F A372090 a(n) = 4^n*binomial((3*n-1)/2, n)*hypergeom([(1-n)/2, -n/2], [(1-3*n)/2], -1)/(n+1). - _Stefano Spezia_, Apr 18 2024
%o A372090 (PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2+k-1/2, k)*binomial(k, n-k))/(n+1);
%Y A372090 Cf. A372091.
%K A372090 nonn
%O A372090 0,2
%A A372090 _Seiichi Manyama_, Apr 17 2024