A131846 - OEIS

%I #26 Apr 20 2017 08:49:59

%S 1,5,55,755,11605,191105,3296755,58810055,1075986505,20079780605,

%T 380733295855,7314056109755,142049912523805,2784519380488505,

%U 55019843803653355,1094695713838691855,21912997682690751505,440999873506064578805,8917597017732200569255

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

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

%H G. C. Greubel, <a href="/A131846/b131846.txt">Table of n, a(n) for n = 1..745</a>

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

%F Recurrence: n*a(n) = 11*(2*n-3)*a(n-1) - (n-3)*a(n-2). - _Vaclav Kotesovec_, Aug 20 2013

%F a(n) ~ sqrt(11*sqrt(30)-60) * (11+2*sqrt(30))^n/(12*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Aug 20 2013

%F From _Ilya Gutkovskiy_, Apr 20 2017: (Start)

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

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

%t Rest[CoefficientList[InverseSeries[Series[x*(1-6*x)/(1-x),{x,0,20}],x],x]] (* _Vaclav Kotesovec_, Aug 20 2013 *)

%o (PARI) Vec(serreverse(x*(1-6*x)/(1-x)+O(x^66))) /* _Joerg Arndt_, Feb 06 2013 */

%K nonn

%O 1,2

%A _Philippe Deléham_, Oct 29 2007

%E More terms from _Philippe Deléham_, Feb 06 2013

%E Offset corrected, _Joerg Arndt_, Feb 15 2013