A364408 G.f. satisfies A(x) = 1 + x*(1 + 1/A(x)^4).

1, 2, -8, 72, -768, 9072, -114240, 1502976, -20414208, 284083968, -4029438976, 58040074752, -846682968064, 12483389708288, -185725854932992, 2784798982701056, -42039464045854720, 638415031298588672, -9746180768647217152, 149486708349609050112

Offset: 0

Author

Seiichi Manyama, Jul 23 2023

Keywords

• sign

Crossrefs

Cf. A364393, A364407, A364409.

Cf. A349311.

Programs

PARI

a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(n+4*k-2, n-1))/n);

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A349311.

a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(n+4*k-2,n-1) for n > 0.