A131869 - OEIS

%I #29 Apr 20 2017 08:50:07

%S 1,7,105,1967,41265,927479,21838425,531731935,13278739425,

%T 338235642983,8753720757705,229531493157519,6084679071674385,

%U 162802128960940119,4390789738688043705,119242319290800424383,3258012200816503807425,89495966923044854350535,2470171286283446551216425

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

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

%H G. C. Greubel, <a href="/A131869/b131869.txt">Table of n, a(n) for n = 1..675</a>

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

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

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

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

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

%F 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

%t Rest[CoefficientList[InverseSeries[Series[x*(1-8*x)/(1-x),{x,0,20}],x],x]] (* _Vaclav Kotesovec_, Aug 20 2013 *)

%o (PARI) Vec(serreverse(x*(1-8*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