A131846 Expansion of series reversion of x*(1-6*x)/(1-x).

1, 5, 55, 755, 11605, 191105, 3296755, 58810055, 1075986505, 20079780605, 380733295855, 7314056109755, 142049912523805, 2784519380488505, 55019843803653355, 1094695713838691855, 21912997682690751505, 440999873506064578805, 8917597017732200569255

Offset

1,2

Comments

The Hankel transform of this sequence is 30^C(n+1,2).

Links

G. C. Greubel, Table of n, a(n) for n = 1..745

Formula

a(n) = Sum_{k=0..n} A086810(n,k)*5^k .

Recurrence: n*a(n) = 11*(2*n-3)*a(n-1) - (n-3)*a(n-2). - Vaclav Kotesovec, Aug 20 2013

a(n) ~ sqrt(11*sqrt(30)-60) * (11+2*sqrt(30))^n/(12*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Aug 20 2013

From Ilya Gutkovskiy, Apr 20 2017: (Start)

G.f.: (1 + x - sqrt(1 - 22*x + x^2))/12.

G.f.: x/(1 - 5*x/(1 - 6*x/(1 - 5*x/(1 - 6*x/(1 - 5*x/(1 - ...)))))), a continued fraction. (End)

Mathematica

Rest[CoefficientList[InverseSeries[Series[x*(1-6*x)/(1-x), {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 20 2013 *)

Prog

(PARI) Vec(serreverse(x*(1-6*x)/(1-x)+O(x^66))) /* Joerg Arndt, Feb 06 2013 */

Crossrefs

Sequence in context: A358955 A292805 A112019 * A144577 A234508 A132865

Adjacent sequences: A131843 A131844 A131845 * A131847 A131848 A131849

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