A058004 Number of 6 X 6 matrices with entries mod n, up to row and column permutation.

1, 251610, 302752867740, 9178323524804624, 28125393244553141210, 19909522361922032493690, 5116530046996205504668323, 626072069382507442113224128, 43460016875695276108491159279

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-A058003, A002724, A052271, A052272.

Row n=6 of A246106.

Formula

a(n)=(1/6!^2)*(n^36 + 30*n^30 + 225*n^26 + 170*n^24 + 1350*n^22 + 3225*n^20 + 4075*n^18 + 9900*n^16 + 28500*n^14 + 56048*n^12 + 61020*n^10 + 77616*n^8 + 153840*n^6 + 87840*n^4 + 34560*n^2).