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Row 5 of array in A212801.
2

%I #21 Jul 04 2018 01:56:56

%S 1,121,5611,193721,6050000,183990301,5598183221,171567260161,

%T 5290933752571,163756656800000,5076226921767101,157423577321804321,

%U 4881873153941565211,151371085451034210421,4692977668021522550000,145487069742178319930401

%N Row 5 of array in A212801.

%C Number of Eulerian circuits in the Cartesian product of two directed cycles of lengths 5 and n. - _Andrew Howroyd_, Jan 12 2018

%H Andrew Howroyd, <a href="/A212802/b212802.txt">Table of n, a(n) for n = 1..200</a>

%H Germain Kreweras, <a href="https://dx.doi.org/10.1016/0095-8956(78)90021-7">Complexité et circuits Eulériens dans les sommes tensorielles de graphes</a>, J. Combin. Theory, B 24 (1978), 202-212.

%F From _Andrew Howroyd_, Jan 12 2018: (Start)

%F Empirical: a(n) = 121*a(n-1) - 6520*a(n-2) + 209330*a(n-3) - 4493120*a(n-4) + 68446433*a(n-5) - 766303183*a(n-6) + 6438802040*a(n-7) - 41070618160*a(n-8) + 199602863240*a(n-9) - 736417358863*a(n-10) + 2039087685503*a(n-11) - 4149490675520*a(n-12) + 5992940178830*a(n-13) - 5786524000120*a(n-14) + 3329026307431*a(n-15) - 852891037441*a(n-16) for n > 16.

%F Empirical g.f.: x*(1 - 31*x^2)*(1 - 2479*x^2 + 94380*x^3 - 1719180*x^4 + 18597458*x^5 - 128373600*x^6 + 576521198*x^7 - 1652131980*x^8 + 2811674580*x^9 - 2289408559*x^10 + 887503681*x^12)/((1 - x)*(1 - 31*x)*(1 - 12*x + 31*x^2)*(1 - 9*x + 31*x^2 - 49*x^3 + 31*x^4)*(1 - 19*x + 151*x^2 - 589*x^3 + 961*x^4)*(1 - 49*x + 961*x^2 - 8649*x^3 + 29791*x^4)).

%F (End)

%t T[m_, n_] := Product[2 - Exp[2*I*h*Pi/m] - Exp[2*I*k*Pi/n], {h, 1, m - 1}, {k, 1, n - 1}];

%t a[n_] := T[5, n] // Round;

%t Array[a, 20] (* _Jean-François Alcover_, Jul 04 2018 *)

%Y Cf. A212801.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, May 27 2012