A378692 G.f. A(x) satisfies A(x) = 1 + x*A(x)^7/(1 - x*A(x)).

1, 1, 8, 86, 1075, 14667, 211799, 3182454, 49243854, 779379652, 12558073022, 205312307834, 3397359326116, 56790504859929, 957574385205771, 16267419813629731, 278162968238908681, 4783813617177604232, 82691541747420586716, 1435895455224032519430, 25035634270828781060188

Offset: 0

Author

Seiichi Manyama, Dec 04 2024

Keywords

• nonn

Crossrefs

Cf. A000108, A001003, A108447, A364747, A364748, A378691.

Cf. A378686, A378690, A378693.

Cf. A378685, A378688, A378694.

Programs

PARI

a(n, r=1, s=1, t=7, u=1) = 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))).

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).