A378693 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(7/6)/(1 - x*A(x)) )^6.

1, 6, 63, 806, 11445, 173388, 2745470, 44891118, 752141682, 12845874594, 222813745704, 3914269052736, 69501455945987, 1245309605501088, 22488056019050124, 408861223600687710, 7478056231521533658, 137496627558561863460, 2540015518588821201453

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

G.f.: A(x) = B(x)^6 where B(x) is the g.f. of A378694.

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=6, 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. A378686, A378690, A378692.

Cf. A378694.

Sequence in context: A346581 A210987 A341376 * A234465 A231552 A302103

Adjacent sequences: A378690 A378691 A378692 * A378694 A378695 A378697

Keyword

nonn,new

Author

Seiichi Manyama, Dec 04 2024

Status

approved