A131521 Expansion of 9/(4 + 5*sqrt(1-36*x)).

1, 10, 190, 4420, 113950, 3128140, 89608780, 2647358920, 80065458910, 2466432898300, 77115832253380, 2440820453410360, 78053018025315340, 2517915855707814520, 81839894422876183000, 2677554649095487584400

Offset: 0

Author

Philippe Deléham, Aug 23 2007

Keywords

• nonn

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..640

Crossrefs

Column k=10 of A183135.

Cf. A039599, A135321.

Programs

Mathematica

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

PARI

Vec(9/(4 + 5*sqrt(1-36*x)) + O(x^50)) \\ G. C. Greubel, Jan 28 2017

Formula

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

a(n) = Sum_{k=0..n} A039599(n,k)*9^(n-k). - Philippe Deléham, Aug 25 2007

a(n) ~ 45*36^n/(32*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 29 2013

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

Extensions

More terms from Olivier Gérard, Sep 22 2007