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 A372035 #10 Apr 17 2024 08:33:44
%S A372035 1,2,4,6,6,2,-4,-2,20,50,24,-130,-302,-14,1176,2166,-874,-10494,
%T A372035 -15464,15886,95006,107586,-210624,-860234,-686084,2499602,7733116,
%U A372035 3460038,-27992190,-68487790,-3894404,301924750,592203732,-243714366,-3165123736,-4936196082
%N A372035 G.f. A(x) satisfies A(x) = ( 1 + 4*x*A(x)/(1 - x) )^(1/2).
%F A372035 G.f.: A(x) = (1-x)/(-2*x + sqrt(1-2*x+5*x^2)).
%F A372035 a(n) = Sum_{k=0..n} 4^k * binomial(k/2+1/2,k) * binomial(n-1,n-k)/(k+1).
%F A372035 a(n) = 2 * A371888(n) for n > 0.
%o A372035 (PARI) my(N=40, x='x+O('x^N)); Vec((1-x)/(-2*x+sqrt(1-2*x+5*x^2)))
%o A372035 (PARI) a(n) = sum(k=0, n, 4^k*binomial(k/2+1/2, k)*binomial(n-1, n-k)/(k+1));
%Y A372035 Cf. A371888, A372016.
%K A372035 sign
%O A372035 0,2
%A A372035 _Seiichi Manyama_, Apr 16 2024