A277665 5th-order coefficients of the 1/N-expansion of traces of negative powers of real Wishart matrices with parameter c=2.

0, 0, 42, 6426, 291696, 7786680, 152881422, 2451889734, 34052988736, 424606263984, 4868397305884, 52193110266396, 529596113392928, 5132630490667056, 47846123752559076, 431382289963465044, 3778388016547646976, 32265703705734047808, 269434703704642529046, 2205554182120984631622

Offset

0,3

Comments

These numbers provide the 5th 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

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).

Formula

G.f.: -(2*z*(96*z^7 - 456*z^6 + 2992*z^5 - 7068*z^4 + 3089*z^3 + 8214*z^2 + 979*z + 12)) / (y(z)^(13/2)) - (2*z*(288*z^8 + 776*z^7 - 336*z^6 - 2916*z^5 + 6276*z^4 - 1312*z^3 - 7560*z^2 - 964*z - 12)) / (y(z)^7), where y(z) = z^2-6*z+1.

Mathematica

y[z] := z^2 - 6*z + 1; CoefficientList[Series[-(2*z*(96*z^7 - 456*z^6 + 2992*z^5 - 7068*z^4 + 3089*z^3 + 8214*z^2 + 979*z + 12))/(y[z]^(13/2)) - (2*z*(288*z^8 + 776*z^7 - 336*z^6 - 2916*z^5 + 6276*z^4 - 1312*z^3 - 7560*z^2 - 964*z - 12))/(y[z]^7), {z, 0, 50}], z] (* G. C. Greubel, Jan 29 2017 *)

Crossrefs

Cf. A006318 (0th order), A277661 (1st order), A277662 (2nd order), A277663 (3rd order), A277664 (4th order).

Sequence in context: A273628 A005791 A167668 * A215837 A211908 A246621

Adjacent sequences: A277662 A277663 A277664 * A277666 A277667 A277668

Keyword

nonn

Author

Fabio Deelan Cunden, Oct 26 2016

Extensions

More terms from Michel Marcus, Oct 30 2016

Status

approved