A130979 G.f.: 7/(3 + 4*sqrt(1-28*x)).

1, 8, 120, 2192, 44248, 949488, 21237168, 489517344, 11544312984, 277190766896, 6753051796240, 166505875155936, 4146984734796016, 104174408364697952, 2636346768784492128, 67149645964991840832, 1720072455615130558488

Offset: 0

Author

Philippe Deléham, Aug 23 2007

Keywords

• nonn

Comments

Number of walks of length 2n on the 8-regular tree beginning and ending at some fixed vertex. Hankel transform is A135315. - Philippe Deléham, Feb 25 2009

Links

• G. C. Greubel, Table of n, a(n) for n = 0..690

Crossrefs

Column k=8 of A183135.

Programs

Mathematica

CoefficientList[Series[7/(3 + 4*Sqrt[1 - 28*x]), {x,0,50}], x] (* G. C. Greubel, Jan 28 2017 *)

PARI

Vec(7/(3 + 4*sqrt(1-28*x)) + O(x^50)) \\ G. C. Greubel, Jan 28 2017

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*7^(n-k). - Philippe Deléham, Aug 25 2007

a(n) ~ 14*28^n/(9*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 29 2013

D-finite with recurrence: n*a(n) +2*(-46*n+21)*a(n-1) +896*(2*n-3)*a(n-2)=0. - R. J. Mathar, Jan 20 2020

Extensions

More terms from Olivier Gérard, Sep 22 2007