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 A372037 #9 Apr 17 2024 08:33:53
%S A372037 1,2,4,4,0,-8,-8,16,48,0,-192,-256,480,1792,320,-7808,-12544,19200,
%T A372037 87808,33280,-382464,-720896,854016,4870144,2844160,-20553728,
%U A372037 -44909568,38967296,289456128,228986880,-1163309056,-2932514816,1701978112,17951686656,17979965440
%N A372037 G.f. A(x) satisfies A(x) = ( 1 + 4*x*(1 + x)*A(x) )^(1/2).
%F A372037 G.f.: A(x) = 1/(-2*x*(1+x) + sqrt(1+(2*x*(1+x))^2)).
%F A372037 a(n) = Sum_{k=0..n} 4^k * binomial(k/2+1/2,k) * binomial(k,n-k)/(k+1).
%o A372037 (PARI) my(N=40, x='x+O('x^N)); Vec(1/(-2*x*(1+x)+sqrt(1+(2*x*(1+x))^2)))
%o A372037 (PARI) a(n) = sum(k=0, n, 4^k*binomial(k/2+1/2, k)*binomial(k, n-k)/(k+1));
%Y A372037 Cf. A372035.
%K A372037 sign
%O A372037 0,2
%A A372037 _Seiichi Manyama_, Apr 16 2024