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A277662
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2nd-order coefficients of the 1/N-expansion of traces of negative powers of real Wishart matrices with parameter c=2.
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6
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0, 0, 6, 102, 1142, 10650, 89576, 705012, 5297924, 38478492, 272262050, 1887071274, 12862479402, 86468603910, 574580180020, 3780504491400, 24663229376872, 159709443132888, 1027505285362590, 6572573611318158, 41827041105943870, 264959521695360786, 1671472578046156512, 10504743400858155708
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OFFSET
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0,3
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COMMENTS
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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.)
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
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).
J. Kuipers, M. Sieber and D. Savin, Efficient semiclassical approach for time delays, New J. Phys. 16 (2014), 123018.
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FORMULA
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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)).
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
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A006318 (0th order), A277661 (1st order), A277663 (3rd order), A277664 (4th order), A277665 (5th order).
Sequence in context: A065990 A306406 A344400 * A022025 A302911 A174481
Adjacent sequences: A277659 A277660 A277661 * A277663 A277664 A277665
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KEYWORD
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nonn
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AUTHOR
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Fabio Deelan Cunden, Oct 26 2016
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EXTENSIONS
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More terms from Michael De Vlieger, Oct 26 2016
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STATUS
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approved
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