A131869 Expansion of series reversion of x*(1-8*x)/(1-x).

1, 7, 105, 1967, 41265, 927479, 21838425, 531731935, 13278739425, 338235642983, 8753720757705, 229531493157519, 6084679071674385, 162802128960940119, 4390789738688043705, 119242319290800424383, 3258012200816503807425, 89495966923044854350535, 2470171286283446551216425

Offset: 1

Author

Philippe Deléham, Oct 29 2007

Keywords

• nonn

Comments

The Hankel transform of this sequence is 56^C(n+1,2) .

Links

• G. C. Greubel, Table of n, a(n) for n = 1..675

Programs

Mathematica

Rest[CoefficientList[InverseSeries[Series[x*(1-8*x)/(1-x),{x,0,20}],x],x]] (* Vaclav Kotesovec, Aug 20 2013 *)

PARI

Vec(serreverse(x*(1-8*x)/(1-x)+O(x^66))) /* Joerg Arndt, Feb 06 2013 */

Formula

a(n) = Sum_{k=0..n} A086810(n,k)*7^k.

From Vaclav Kotesovec, Aug 20 2013: (Start)

G.f.: (x-15-sqrt(x^2-30*x+1))/16.

Recurrence: n*a(n) = 15*(2*n-3)*a(n-1) - (n-3)*a(n-2).

a(n) ~ sqrt(30*sqrt(14)-112)*(15+4*sqrt(14))^n/(16*sqrt(Pi)*n^(3/2)). (End)

G.f.: x/(1 - 7*x/(1 - 8*x/(1 - 7*x/(1 - 8*x/(1 - 7*x/(1 - ...)))))), a continued fraction. - Ilya Gutkovskiy, Apr 20 2017

Extensions

More terms from Philippe Deléham, Feb 06 2013

Offset corrected, Joerg Arndt, Feb 15 2013