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A277663
3rd-order coefficients of the 1/N-expansion of traces of negative powers of real Wishart matrices with parameter c=2.
6
0, 0, 10, 378, 7048, 96000, 1092460, 11060700, 103150528, 905077728, 7576640950, 61098854454, 477942694136, 3645484792560, 27220292840440, 199588002587160, 1440630859132416, 10256896070590464, 72150109176698562, 502120765832371602, 3461203073248719400, 23654601049848668256
OFFSET
0,3
COMMENTS
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.)
LINKS
F. D. Cunden, F. Mezzadri, N. Simm and P. Vivo, Large-N expansion for the time-delay matrix of ballistic chaotic cavities, J. Math. Phys. 57, 111901 (2016). E-print arXiv:1607.00250.
J. Kuipers, M. Sieber and D. Savin, Efficient semiclassical approach for time delays, New J. Phys. 16, 123018 (2014), arXiv:1409.1532 [nlin.CD], 2014.
FORMULA
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.
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
MATHEMATICA
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 *)
CROSSREFS
Cf. A006318 (0th order), A277661 (1st order), A277662 (2nd order), A277664 (4th order), A277665 (5th order).
Sequence in context: A358801 A117312 A200804 * A000591 A131312 A055733
KEYWORD
nonn
AUTHOR
Fabio Deelan Cunden, Oct 26 2016
STATUS
approved