A366501 G.f. A(x) satisfies A(x) = 1 + x / ((1+x)^4*A(x)^3).

1, 1, -7, 49, -399, 3633, -35511, 363937, -3858079, 41951521, -465296487, 5243459409, -59865074223, 690979478481, -8049598938135, 94522387901505, -1117615459764031, 13294669980012865, -158995530738069703, 1910555096402418545, -23056131790988675279

Offset: 0

Author

Seiichi Manyama, Oct 11 2023

Keywords

• sign

Crossrefs

Cf. A001006, A366221, A366272, A366273, A366495, A366496, A366497, A366498, A366499, A366500.

Cf. A213336.

Programs

PARI

a(n) = (-1)^(n-1)*sum(k=0, n, binomial(n+3*k-1, n-k)*binomial(4*k-1, k)/(4*k-1));

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A213336.

a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(n+3*k-1,n-k) * binomial(4*k-1,k) / (4*k-1).