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G.f.: 12/(5 + 7*sqrt(1-24*x)).
6

%I #20 Jan 30 2020 21:29:16

%S 1,7,91,1435,24955,460747,8859739,175466347,3553964155,73266506635,

%T 1532152991131,32420721097387,692865048943291,14932919812627915,

%U 324195908270339035,7083228794200550635

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

%C 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

%H Vincenzo Librandi, <a href="/A130978/b130978.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = Sum_{k=0..n} A039599(n,k)*6^(n-k). - _Philippe Deléham_, Aug 25 2007

%F 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

%F a(n) ~ 7*2^(3*n+1)*3^(n+1)/(25*sqrt(Pi)*n^(3/2)) . - _Vaclav Kotesovec_, Oct 20 2012

%p 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

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

%Y Column k=7 of A183135.

%K nonn

%O 0,2

%A _Philippe Deléham_, Aug 23 2007

%E More terms from _Emeric Deutsch_, Aug 26 2007