A378685 G.f. A(x) satisfies A(x) = 1 + x*A(x)^7/(1 - x*A(x)^3).

1, 1, 8, 88, 1126, 15716, 232069, 3564835, 56382489, 912031280, 15018257510, 250913307393, 4242722219425, 72470224174650, 1248608968982903, 21673752440979879, 378677335852165297, 6654158090059397480, 117523324766568499072, 2085095374834405245007

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)^3)).

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=3) = 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. A243659, A300048.

Cf. A108447, A365192.

Cf. A378686.

Sequence in context: A247738 A115864 A036917 * A003497 A051605 A271268

Adjacent sequences: A378679 A378680 A378681 * A378686 A378687 A378688

Keyword

nonn,new

Author

Seiichi Manyama, Dec 04 2024

Status

approved