A366363 G.f. satisfies A(x) = (1 + x/A(x))/(1 - x).

1, 2, 0, 4, -8, 32, -112, 432, -1696, 6848, -28160, 117632, -497664, 2128128, -9183488, 39940864, -174897664, 770452480, -3411959808, 15181264896, -67833868288, 304256253952, -1369404661760, 6182858317824, -27995941060608, 127100310290432, -578433619525632

Offset: 0

Author

Seiichi Manyama, Oct 08 2023

Keywords

• sign

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A346626, A349310, A349311, A349312, A349313, A349314, A366364, A366365, A366366.

Cf. A366356.

Programs

Mathematica

A366363[n_]:=(-1)^(n-1)Sum[Binomial[2k-1,k]Binomial[k-1,n-k]/(2k-1),{k,0,n}];
Array[A366363,30,0] (* Paolo Xausa, Oct 20 2023 *)

PARI

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

Formula

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

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