%I #28 Oct 20 2023 06:45:01

%S 1,3,2,8,-9,62,-230,1054,-4753,22208,-105419,508396,-2482284,12248430,

%T -60980860,305955372,-1545397447,7852100312,-40105277621,205798130624,

%U -1060467961487,5485199090834,-28469067353663,148220323891484,-773892318396664,4051261817405034

%N G.f. satisfies A(x) = (1 + x/A(x))/(1 - x)^2.

%H Paolo Xausa, <a href="/A363816/b363816.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: A(x) = -2*x / (1-sqrt(1+4*x*(1-x)^2)).

%F a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(2*k-1,k) * binomial(2*(k-1),n-k)/(2*k-1).

%t A363816[n_]:=(-1)^(n-1)Sum[Binomial[2k-1,k]Binomial[2(k-1),n-k]/(2k-1),{k,0,n}];Array[A363816,30,0] (* _Paolo Xausa_, Oct 20 2023 *)

%o (PARI) a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(2*(k-1), n-k)/(2*k-1));

%Y Partial sums of A366356.

%Y Cf. A162477, A363818, A364629, A364630.

%Y Cf. A363817, A366363.

%K sign

%O 0,2

%A _Seiichi Manyama_, Oct 18 2023