A130980 G.f.: 16/(7 + 9*sqrt(1 - 32*x)).

1, 9, 153, 3177, 73017, 1785609, 45543897, 1197639081, 32231934585, 883404542025, 24570973169433, 691759954058985, 19674867844155321, 564462038150345097, 16315646312285498457, 474680922491822688297

Offset: 0

Author

Philippe Deléham, Aug 23 2007

Keywords

• nonn

Comments

Number of walks of length 2n on the 9-regular tree beginning and ending at some fixed vertex. Hankel transform is A135320. - Philippe Deléham, Feb 25 2009

Links

• G. C. Greubel, Table of n, a(n) for n = 0..660

Crossrefs

Column k=9 of A183135.

Programs

Mathematica

CoefficientList[Series[16/(7+9*Sqrt[1-32*x]),{x,0,30}],x] (* Harvey P. Dale, Feb 21 2013 *)

PARI

Vec(16/(7 + 9*sqrt(1-32*x)) + O(x^50)) \\ G. C. Greubel, Jan 28 2017

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*8^(n-k). - Philippe Deléham, Aug 25 2007

a(n) ~ 72/49*32^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 29 2013

D-finite with recurrence: n*a(n) +(-113*n+48)*a(n-1) +1296*(2*n-3)*a(n-2)=0. - R. J. Mathar, Jan 20 2020

Extensions

More terms from Olivier Gérard, Sep 22 2007