A378694 G.f. A(x) satisfies A(x) = 1 + x*A(x)^7/(1 - x*A(x)^6).

1, 1, 8, 91, 1210, 17577, 270314, 4326070, 71300386, 1202012254, 20630488004, 359279348424, 6332747550808, 112761701957119, 2025325557546780, 36650364776763804, 667570101840389826, 12229542931765845994, 225183117821591853440, 4165207037639796288385

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

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).

Prog

(PARI) a(n, r=1, s=1, t=7, u=6) = 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));

Crossrefs

Cf. A378685, A378688, A378692.

Sequence in context: A184709 A190943 A180912 * A234280 A298013 A302614

Adjacent sequences: A378691 A378692 A378693 * A378695 A378696 A378697

Keyword

nonn

Author

Seiichi Manyama, Dec 04 2024

Status

approved