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Expansion of 9/(4 + 5*sqrt(1-36*x)).
6

%I #28 Jan 30 2020 21:29:16

%S 1,10,190,4420,113950,3128140,89608780,2647358920,80065458910,

%T 2466432898300,77115832253380,2440820453410360,78053018025315340,

%U 2517915855707814520,81839894422876183000,2677554649095487584400

%N Expansion of 9/(4 + 5*sqrt(1-36*x)).

%C Number of walks of length 2n on the 10-regular tree beginning and ending at some fixed vertex. Hankel transform is A135321. - _Philippe Deléham_, Feb 25 2009

%H G. C. Greubel, <a href="/A131521/b131521.txt">Table of n, a(n) for n = 0..640</a>

%F G.f.: 9/(4 + 5*sqrt(1-36*x)).

%F a(n) = Sum_{k=0..n} A039599(n,k)*9^(n-k). - _Philippe Deléham_, Aug 25 2007

%F a(n) ~ 45*36^n/(32*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Jun 29 2013

%F D-finite with recurrence: n*a(n) +2*(-68*n+27)*a(n-1) +1800*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Jan 20 2020

%t CoefficientList[Series[9/(4+5*Sqrt[1-36*x]),{x,0,30}],x] (* _Harvey P. Dale_, Aug 21 2012 *)

%o (PARI) Vec(9/(4 + 5*sqrt(1-36*x)) + O(x^50)) \\ _G. C. Greubel_, Jan 28 2017

%Y Column k=10 of A183135.

%Y Cf. A039599, A135321.

%K nonn

%O 0,2

%A _Philippe Deléham_, Aug 23 2007

%E More terms from _Olivier Gérard_, Sep 22 2007