A365110 G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^3.

1, 1, -3, 3, 11, -54, 66, 297, -1575, 1980, 10300, -55392, 68352, 403583, -2153685, 2551845, 16999045, -89142087, 99986901, 750955382, -3850437018, 4041467331, 34310059311, -171533033904, 166630375248, 1607168518073, -7821913867611, 6950050797297

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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).

Prog

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

Crossrefs

Cf. A007440, A365109, A365111, A365112.

Cf. A365086.

Sequence in context: A200861 A113892 A334283 * A350921 A352857 A352582

Adjacent sequences: A365107 A365108 A365109 * A365111 A365112 A365113

Keyword

sign

Author

Seiichi Manyama, Aug 22 2023

Status

approved