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 A378668 #15 Dec 04 2024 08:39:37
%S A378668 1,2,13,112,1104,11778,132374,1543740,18505996,226632616,2823110349,
%T A378668 35659080952,455652487060,5879489288828,76502741016012,
%U A378668 1002670573618324,13224761472453756,175404372357915096,2338003752387818372,31302169754776944512,420760252068869028028
%N A378668 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^2/(1 - x*A(x)^2) )^2.
%F A378668 G.f.: exp( 1/2 * Sum_{k>=1} A378613(k) * x^k/k ).
%F A378668 G.f.: B(x)^2 where B(x) is the g.f. of A243667.
%F A378668 a(n) = 2 * Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(n,k) * binomial(4*n+k+2,n)/(4*n+k+2).
%F A378668 a(n) = 2 * Sum_{k=0..n} binomial(4*n+k+2,k) * binomial(n-1,n-k)/(4*n+k+2).
%F A378668 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(5/2)/(1 - x*A(x)^2) )^2.
%o A378668 (PARI) a(n) = 2*sum(k=0, n, 2^k*(-1)^(n-k)*binomial(n, k)*binomial(4*n+k+2, n)/(4*n+k+2));
%o A378668 (PARI) a(n, r=2, s=1, t=5, u=4) = 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 A378668 Cf. A243667, A378610, A378669.
%Y A378668 Cf. A010683, A211789, A378670.
%Y A378668 Cf. A378613.
%K A378668 nonn
%O A378668 0,2
%A A378668 _Seiichi Manyama_, Dec 02 2024