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 A379383 #11 Dec 22 2024 09:06:38
%S A379383 1,2,10,80,750,7680,83252,939008,10905942,129548288,1566565452,
%T A379383 19220267008,238662840780,2993651974144,37876206019560,
%U A379383 482802294325248,6194365014836582,79930063134392320,1036640587694252380,13505632613590630400,176673045664669396132,2319654465118014537728
%N A379383 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x))/(1 - 2*x*A(x)^3) ).
%F A379383 a(n) = 2^n * Sum_{k=0..n} binomial(n/2+2*k-1/2,k) * binomial(n/2+k+1/2,n-k)/(n+2*k+1).
%F A379383 a(n) = 2^n * Sum_{k=0..n} binomial(n,k) * binomial(n/2+2*k+1/2,n)/(n+4*k+1).
%o A379383 (PARI) a(n) = 2^n*sum(k=0, n, binomial(n/2+2*k-1/2, k)*binomial(n/2+k+1/2, n-k)/(n+2*k+1));
%Y A379383 Cf. A138020, A379382.
%Y A379383 Cf. A078531, A379328, A379331.
%K A379383 nonn
%O A379383 0,2
%A A379383 _Seiichi Manyama_, Dec 22 2024