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

%I

%S 1,317,90492,7880456,270656150,4947097821,58002778967,490172624992,

%T 3223155968811,17382581357725,79840867013666,321169288917192,

%U 1155731257886192,3782368364610941,11406226119319725,32031530635953536,84493500676300117,210856844364222717

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

%C 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.

%H Alois P. Heinz, <a href="/A058002/b058002.txt">Table of n, a(n) for n = 1..1000</a>

%F 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).

%F G.f.: -x*(x +1)*(x^14 +299*x^13 +84940*x^12 +6299584*x^11 +142482546*x^10 +1214416453*x^9 +4351647617*x^8 +6732281120*x^7 +4351647617*x^6 +1214416453*x^5 +142482546*x^4 +6299584*x^3 +84940*x^2 +299*x +1) / (x -1)^17. - _Colin Barker_, Jul 09 2013

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

%Y Row n=4 of A246106.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Nov 04 2000

%E More terms from _Colin Barker_, Jul 09 2013

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)