A130978 G.f.: 12/(5 + 7*sqrt(1-24*x)).

1, 7, 91, 1435, 24955, 460747, 8859739, 175466347, 3553964155, 73266506635, 1532152991131, 32420721097387, 692865048943291, 14932919812627915, 324195908270339035, 7083228794200550635

Offset: 0

Author

Philippe Deléham, Aug 23 2007

Keywords

• nonn

Comments

Number of walks of length 2n on the 7-regular tree beginning and ending at some fixed vertex. Hankel transform is A135314. - Philippe Deléham, Feb 25 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Column k=7 of A183135.

Programs

Maple

g:=12/(5+7*sqrt(1-24*x));gser:=series(g,x=0,20); seq(coeff(gser,x,n),n=0..15); # Emeric Deutsch, Aug 26 2007

Mathematica

CoefficientList[Series[12/(5+7*Sqrt[1-24*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*6^(n-k). - Philippe Deléham, Aug 25 2007

D-finite with recurrence: n*a(n) = (73*n-36)*a(n-1) - 588*(2*n-3)*a(n-2) . - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 7*2^(3*n+1)*3^(n+1)/(25*sqrt(Pi)*n^(3/2)) . - Vaclav Kotesovec, Oct 20 2012

Extensions

More terms from Emeric Deutsch, Aug 26 2007