A364409 G.f. satisfies A(x) = 1 + x*(1 + 1/A(x)^5).

1, 2, -10, 110, -1430, 20570, -315282, 5047350, -83406510, 1411954610, -24360750810, 426796726334, -7572551327430, 135790011411850, -2457028916693090, 44804882306441990, -822573909558939998, 15191515999168557410, -282038057756813698730

Offset: 0

Author

Seiichi Manyama, Jul 23 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..769

Crossrefs

Cf. A112478, A364393, A364407, A364408, A366266, A366267, A366268.

Cf. A349312.

Programs

PARI

a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(n+5*k-2, n-1))/n);

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A349312.

a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(n+5*k-2,n-1) for n > 0.