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%I #27 Feb 01 2021 02:06:04
%S 0,0,6,102,1142,10650,89576,705012,5297924,38478492,272262050,
%T 1887071274,12862479402,86468603910,574580180020,3780504491400,
%U 24663229376872,159709443132888,1027505285362590,6572573611318158,41827041105943870,264959521695360786,1671472578046156512,10504743400858155708
%N 2nd-order coefficients of the 1/N-expansion of traces of negative powers of real Wishart matrices with parameter c=2.
%C These numbers provide the 2nd order of the 1/N-expansion of traces of powers of a random time-delay matrix in presence of time-reversal symmetry. (The 0th order is given by the Large Schröder numbers A006318.)
%H G. C. Greubel, <a href="/A277662/b277662.txt">Table of n, a(n) for n = 0..1000</a>
%H F. D. Cunden, F. Mezzadri, N. Simm and P. Vivo, <a href="http://scitation.aip.org/content/aip/journal/jmp/57/11/10.1063/1.4966642">Large-N expansion for the time-delay matrix of ballistic chaotic cavities</a>, J. Math. Phys. 57, 111901 (2016).
%H J. Kuipers, M. Sieber and D. Savin, <a href="http://dx.doi.org/10.1088/1367-2630/16/12/123018">Efficient semiclassical approach for time delays</a>, New J. Phys. 16 (2014), 123018.
%F G.f.: (x^2-3*x)/((x^2-6*x+1)^2)+(3*x^3-4*x^2+3 x)/((x^2-6*x+1)^(5/2)).
%F a(n) ~ 7*(3*sqrt(2)+4)^(5/2) * n^(3/2) * (1+sqrt(2))^(2*n-4) / (3*2^(9/2)*sqrt(Pi)) * (1 - (3*sqrt((2+3/sqrt(2))*Pi))/(7*sqrt(n))). - _Vaclav Kotesovec_, Oct 27 2016
%t CoefficientList[Series[(x^2 - 3 x)/((x^2 - 6 x + 1)^2) + (3 x^3 - 4 x^2 + 3 x)/((x^2 - 6 x + 1)^(5/2)), {x, 0, 23}], x] (* _Michael De Vlieger_, Oct 26 2016 *)
%Y Cf. A006318 (0th order), A277661 (1st order), A277663 (3rd order), A277664 (4th order), A277665 (5th order).
%K nonn
%O 0,3
%A _Fabio Deelan Cunden_, Oct 26 2016
%E More terms from _Michael De Vlieger_, Oct 26 2016
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