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 A370479 #13 Mar 31 2024 08:46:04
%S A370479 1,2,9,40,184,872,4232,20936,105208,535624,2757000,14324456,75028152,
%T A370479 395750568,2100380424,11208429960,60103977976,323708642952,
%U A370479 1750294676744,9497584905128,51703651336888,282302043458536,1545558070957960,8482843567140680
%N A370479 G.f. satisfies A(x) = ( 1 + x * (A(x)^(1/2) / (1-x))^2 )^2.
%F A370479 G.f.: B(x)^2 where B(x) is the g.f. of A006319.
%F A370479 a(n) = 2 * Sum_{k=0..n} binomial(2*k+2,k) * binomial(n+k-1,n-k)/(2*k+2).
%o A370479 (PARI) my(N=30, x='x+O('x^N)); Vec((1+x*((1-x-sqrt(1-6*x+x^2))/(2*x))^2)^2)
%o A370479 (PARI) a(n, r=2, s=2, t=2, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
%Y A370479 Cf. A045623, A370477.
%Y A370479 Cf. A006319, A370480.
%K A370479 nonn
%O A370479 0,2
%A A370479 _Seiichi Manyama_, Mar 31 2024