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a(n) = n! (2*sum(1..n-1))!.
2

%I #3 Mar 31 2012 10:22:03

%S 1,4,4320,11496038400,291948240981196800000,

%T 190982059064777562218142105600000000,

%U 7081230833474514688657438735472338312479375360000000000

%N a(n) = n! (2*sum(1..n-1))!.

%C Number of distinct n x n matrices containing n^2 different elements which have that same trace.

%t Table[n! (2*Sum[x, {x, 1, n - 1}])!, {n, 1, 10}]

%Y Cf. A127233, A127234.

%K nonn

%O 1,2

%A _Artur Jasinski_, Jan 09 2007, Jan 11 2007