A378688 G.f. A(x) satisfies A(x) = 1 + x*A(x)^7/(1 - x*A(x)^2).

1, 1, 8, 87, 1100, 15173, 221449, 3362472, 52571486, 840658030, 13685005046, 226034078091, 3778561589470, 63808500324629, 1086892630726300, 18652582726212792, 322197108441548095, 5597514211552503858, 97741241871353705160, 1714482398765781043424

Offset: 0

Author

Seiichi Manyama, Dec 04 2024

Keywords

• nonn

Crossrefs

Cf. A378690.

Programs

PARI

a(n, r=1, s=1, t=7, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Formula

G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^6/(1 - x*A(x)^2)).

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