A365112 G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^5.

1, 1, -5, 10, 20, -220, 624, 940, -15220, 52090, 49310, -1254070, 4951430, 2039640, -113088840, 505430700, -42379684, -10748423405, 53899438385, -29300595085, -1054751754795, 5914944193114, -5760460624890, -105478270711140, 661900612108440, -914408777470140

Offset: 0

Author

Seiichi Manyama, Aug 22 2023

Keywords

• sign

Crossrefs

Cf. A007440, A365109, A365110, A365111.

Cf. A365088.

Programs

PARI

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

Formula

If g.f. satisfies A(x) = 1 + x/(1 + x*A(x))^s, then a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).