A366356 G.f. satisfies A(x) = 1/(1 - x) + x/A(x).

1, 2, -1, 6, -17, 71, -292, 1284, -5807, 26961, -127627, 613815, -2990680, 14730714, -73229290, 366936232, -1851352819, 9397497759, -47957377933, 245903408245, -1266266092111, 6545667052321, -33954266444497, 176689391245147, -922112642288148, 4825154135801698

Offset: 0

Author

Seiichi Manyama, Oct 08 2023

Keywords

• sign

Links

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

Crossrefs

Partial sums give A363816.

Cf. A007317, A199475, A349289, A349290, A349291, A349292, A349293, A366357, A366358, A366359.

Cf. A112478, A366363.

Programs

Mathematica

A366356[n_]:=(-1)^(n-1)Sum[Binomial[2k-1,k]Binomial[2k-1,n-k]/(2k-1),{k,0,n}];
Array[A366356,30,0] (* Paolo Xausa, Oct 20 2023 *)

PARI

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

Formula

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

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