A363817 G.f. satisfies A(x) = (1 + x/A(x))/(1 - x)^3.

1, 4, 5, 15, -5, 111, -402, 2172, -10892, 57362, -305756, 1656560, -9083341, 50328219, -281324174, 1584578882, -8984740332, 51242962422, -293772467974, 1691974930794, -9785378133066, 56805049768410, -330880419984556, 1933299689139664, -11328101469158229

Offset: 0

Author

Seiichi Manyama, Oct 18 2023

Keywords

• sign

Crossrefs

Cf. A366363, A363816.

Programs

PARI

a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(3*(k-1), n-k)/(2*k-1));

Formula

G.f.: A(x) = -2*x / (1-sqrt(1+4*x*(1-x)^3)).

a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(2*k-1,k) * binomial(3*(k-1),n-k)/(2*k-1).