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%I #26 Feb 01 2021 02:06:00
%S 0,0,2,18,128,840,5306,32802,200064,1209168,7261042,43394802,
%T 258401216,1534310232,9089538922,53748310338,317337926144,
%U 1871206403232,11021718519266,64859423566290,381371547195648,2240888478928488,13159108981577242,77232197285953890,453066998085075840,2656691258873376240
%N 1st-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 1st 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="/A277661/b277661.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.: (1-3*x)/(2*(x^2-6*x+1))-1/(2*(x^2-6*x+1)^(1/2)).
%F a(n) ~ 2^(-5/2) * (3*sqrt(2)-4) * (1+sqrt(2))^(2*n+2) * (1 - 1/(sqrt(Pi*(3*sqrt(2)-4)*n))). - _Vaclav Kotesovec_, Oct 27 2016
%t CoefficientList[Series[(1 - 3 x)/(2 (x^2 - 6 x + 1)) - 1/(2 (x^2 - 6 x + 1)^(1/2)), {x, 0, 25}], x] (* _Michael De Vlieger_, Oct 26 2016 *)
%Y Cf. A006318 (0th order), A277662 (2nd 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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