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%I #24 Jun 05 2021 02:23:09
%S 1,6,66,876,12786,197796,3183156,52718616,892401426,15368638836,
%T 268388185596,4741271556456,84573471344916,1521119577791976,
%U 27554494253636136,502257203287150896,9205363627419463506
%N G.f.: 5/(2 + 3*sqrt(1-20*x)).
%C Number of walks of length 2n on the 6-regular tree beginning and ending at some fixed vertex. Hankel transform is A135349. - _Philippe Deléham_, Feb 25 2009
%H Vincenzo Librandi, <a href="/A130977/b130977.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = Sum_{k=0..n} A039599(n,k)*5^(n-k). - _Philippe Deléham_, Aug 25 2007
%F From _Gary W. Adamson_, Jul 22 2011: (Start)
%F a(n) = upper left term in M^n, M = an infinite square production matrix as follows:
%F 6, 6, 0, 0, 0, 0, ...
%F 5, 5, 5, 0, 0, 0, ...
%F 5, 5, 5, 5, 0, 0, ...
%F 5, 5, 5, 5, 5, 0, ...
%F 5, 5, 5, 5, 5, 5, ...
%F ... (End)
%F D-finite with recurrence: n*a(n) = 2*(28*n-15)*a(n-1) - 360*(2*n-3)*a(n-2). - _Vaclav Kotesovec_, Oct 20 2012
%F a(n) ~ 3*2^(2*n-3)*5^(n+1)/(sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 20 2012
%t CoefficientList[Series[5/(2+3*Sqrt[1-20*x]), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 20 2012 *)
%Y Column k=6 of A183135.
%K nonn
%O 0,2
%A _Philippe Deléham_, Aug 23 2007
%E More terms from _Olivier Gérard_, Sep 22 2007
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