A131926 - OEIS

%I #28 Apr 20 2017 08:50:14

%S 1,6,78,1266,23010,448062,9140118,192804954,4171347258,92051810934,

%T 2063947865694,46885775086338,1076785174781394,24959959877000238,

%U 583201632981980454,13721408509737851754,324797812150741560618,7729580015834558984934,184829586432121709114478

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

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

%H G. C. Greubel, <a href="/A131926/b131926.txt">Table of n, a(n) for n = 1..700</a>

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

%F From _Vaclav Kotesovec_, Aug 20 2013: (Start)

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

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

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

%F 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

%t Rest[CoefficientList[InverseSeries[Series[x*(1-7*x)/(1-x),{x,0,20}],x],x]] (* _Vaclav Kotesovec_, Aug 20 2013 *)

%o (PARI) Vec(serreverse(x*(1-7*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