A365150 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x))^3.

1, 1, 5, 26, 150, 925, 5967, 39772, 271758, 1893431, 13400897, 96078789, 696333585, 5093266409, 37549674939, 278739057687, 2081637677823, 15628794649931, 117897848681271, 893167062280029, 6792410218680749, 51835002735642287, 396821349652564273

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A001003, A011270.

Cf. A365151, A365152.

Cf. A052529.

Programs

PARI

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

Formula

If g.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^s )^t, then a(n) = Sum_{k=0..n} binomial(t*(n+k+1),k) * binomial(n+(s-1)*k-1,n-k)/(n+k+1).

G.f.: (1/x) * Series_Reversion( x*(1 - x/(1 - x)^3) ). - Seiichi Manyama, Sep 24 2024