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 A366363 #17 Oct 20 2023 06:45:10
%S A366363 1,2,0,4,-8,32,-112,432,-1696,6848,-28160,117632,-497664,2128128,
%T A366363 -9183488,39940864,-174897664,770452480,-3411959808,15181264896,
%U A366363 -67833868288,304256253952,-1369404661760,6182858317824,-27995941060608,127100310290432,-578433619525632
%N A366363 G.f. satisfies A(x) = (1 + x/A(x))/(1 - x).
%H A366363 Paolo Xausa, <a href="/A366363/b366363.txt">Table of n, a(n) for n = 0..1000</a>
%F A366363 G.f.: A(x) = -2*x / (1-sqrt(1+4*x*(1-x))).
%F A366363 a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(2*k-1,k) * binomial(k-1,n-k)/(2*k-1).
%t A366363 A366363[n_]:=(-1)^(n-1)Sum[Binomial[2k-1,k]Binomial[k-1,n-k]/(2k-1),{k,0,n}];
%t A366363 Array[A366363,30,0] (* _Paolo Xausa_, Oct 20 2023 *)
%o A366363 (PARI) a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(k-1, n-k)/(2*k-1));
%Y A366363 Cf. A346626, A349310, A349311, A349312, A349313, A349314, A366364, A366365, A366366.
%Y A366363 Cf. A366356.
%K A366363 sign
%O A366363 0,2
%A A366363 _Seiichi Manyama_, Oct 08 2023