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%I #32 Feb 01 2021 02:06:08
%S 0,0,10,378,7048,96000,1092460,11060700,103150528,905077728,
%T 7576640950,61098854454,477942694136,3645484792560,27220292840440,
%U 199588002587160,1440630859132416,10256896070590464,72150109176698562,502120765832371602,3461203073248719400,23654601049848668256
%N 3rd-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 3rd 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="/A277663/b277663.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://arxiv.org/abs/1607.00250">Large-N expansion for the time-delay matrix of ballistic chaotic cavities</a>, J. Math. Phys. 57, 111901 (2016). E-print arXiv:1607.00250.
%H J. Kuipers, M. Sieber and D. Savin, <a href="http://arxiv.org/abs/1409.1532">Efficient semiclassical approach for time delays</a>, New J. Phys. 16, 123018 (2014), arXiv:1409.1532 [nlin.CD], 2014.
%F G.f.: -(2*z)*(2*z^3-9*z^2+19*z+3)/(y(z)^(7/2))-(2*z)*(6*z^4-5*z^3+9*z^2-15*z-3)/(y(z)^4) where y(z)=z^2-6*z+1.
%F a(n) ~ (17*sqrt(2)/24-1) * n^3 * (1+sqrt(2))^(2*n+6) * (1 - (7*sqrt((8+6*sqrt(2)) / Pi))/(8*sqrt(n))). - _Vaclav Kotesovec_, Oct 27 2016
%t CoefficientList[Series[-(2 x) (2 x^3 - 9 x^2 + 19 x + 3) / ((x^2 - 6 x + 1)^(7/2)) - (2 x) (6 x^4 - 5 x^3 + 9 x^2 - 15 x - 3) / ((x^2 - 6 x + 1)^4), {x, 0, 25}], x] (* _Vincenzo Librandi_, Nov 07 2016 *)
%Y Cf. A006318 (0th order), A277661 (1st order), A277662 (2nd order), A277664 (4th order), A277665 (5th order).
%K nonn
%O 0,3
%A _Fabio Deelan Cunden_, Oct 26 2016
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