A131926 Expansion of series reversion of x(1-7x)/(1-x).

1, 6, 78, 1266, 23010, 448062, 9140118, 192804954, 4171347258, 92051810934, 2063947865694, 46885775086338, 1076785174781394, 24959959877000238, 583201632981980454, 13721408509737851754, 324797812150741560618, 7729580015834558984934, 184829586432121709114478

Offset

1,2

Comments

The Hankel transform of this sequence is 42^C(n+1,2) .

Links

G. C. Greubel, Table of n, a(n) for n = 1..700

Formula

a(n) = Sum_{k=0..n} A086810(n,k)*6^k.

From Vaclav Kotesovec, Aug 20 2013: (Start)

G.f.: (x-13-sqrt(x^2-26*x+1))/14.

Recurrence: n*a(n) = 13*(2*n-3)*a(n-1) - (n-3)*a(n-2).

a(n) ~ sqrt(13*sqrt(42)-84)*(13+2*sqrt(42))^n/(14*sqrt(Pi)*n^(3/2)). (End)

G.f.: x/(1 - 6*x/(1 - 7*x/(1 - 6*x/(1 - 7*x/(1 - 6*x/(1 - ...)))))), a continued fraction. - Ilya Gutkovskiy, Apr 20 2017

Mathematica

Rest[CoefficientList[InverseSeries[Series[x*(1-7*x)/(1-x), {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 20 2013 *)

Prog

(PARI) Vec(serreverse(x*(1-7*x)/(1-x)+O(x^66))) /* Joerg Arndt, Feb 06 2013 */

Crossrefs

Sequence in context: A208473 A358956 A268555 * A132866 A279444 A094419

Adjacent sequences: A131923 A131924 A131925 * A131927 A131928 A131929

Keyword

nonn

Author

Philippe Deléham, Oct 29 2007

Extensions

More terms from Philippe Deléham, Feb 06 2013

Offset corrected, Joerg Arndt, Feb 15 2013

Status

approved