A058002 Number of 4 X 4 matrices with entries mod n, up to row and column permutation.

1, 317, 90492, 7880456, 270656150, 4947097821, 58002778967, 490172624992, 3223155968811, 17382581357725, 79840867013666, 321169288917192, 1155731257886192, 3782368364610941, 11406226119319725, 32031530635953536, 84493500676300117, 210856844364222717

Offset: 1

Author

Vladeta Jovovic, Nov 04 2000

Keywords

• easy
• nonn

Comments

Number of k X l matrices with entries mod n, up to row and column permutation is Z(S_k X S_l; n,n,...) where Z(S_k X S_l; x_1,x_2,...) is cycle index of Cartesian product of symmetric groups S_k and S_l of degree k and l, respectively.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A058001, A058003, A058004, A002724, A052271, A052272.

Row n=4 of A246106.

Formula

a(n)=(1/4!^2)*(n^16 + 12*n^12 + 36*n^10 + 67*n^8 + 160*n^6 + 204*n^4 + 96*n^2).

G.f.: -x*(x +1)*(x^14 +299*x^13 +84940*x^12 +6299584*x^11 [phone]*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 +6299584*x^3 +84940*x^2 +299*x +1) / (x -1)^17. - Colin Barker, Jul 09 2013

Extensions

More terms from Colin Barker, Jul 09 2013