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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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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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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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