A058003 Number of 5 X 5 matrices with entries mod n, up to row and column permutation.

1, 5624, 64796982, 79846389608, 20834113243925, 1979525296377132, 93242242505023122, 2625154125717590496, 49871029909245781491, 694584034909225304800, 7525039263469551291908, 66252712846754819753160

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. A039623, A058001, A058002, A058004, A002724, A052271, A052272.

Row n=5 of A246106.

Formula

a(n)=(1/5!^2)*(n^25 + 20*n^20 + 100*n^17 + 70*n^15 + 300*n^14 + 225*n^13 + 400*n^12 + 400*n^11 + 100*n^10 + 1600*n^9 + 2300*n^8 + 1300*n^7 + 1200*n^6 + 1824*n^5 + 480*n^4 + 1680*n^3 + 2400*n^2).

Extensions

More terms from James Sellers, Nov 08 2000