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a(n) = n^n - (-1)^n*(n+1)!.
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%I #6 May 31 2023 15:38:23

%S 3,-2,51,136,3845,41616,863863,16414336,391049289,9960083200,

%T 285790672211,8909873427456,302962284883453,11110699151190016,

%U 437914813170747375,18446388386281455616,827246664260042492177

%N a(n) = n^n - (-1)^n*(n+1)!.

%C Permanent of the (n X n) matrix {1/(x_i-y_j), 1<=i<=n, 1<=j<=n}, where x_1,x_2,...,x_m are the zeros of x^n-1 and y_1,y_2,...,y_m the zeros of y^(n+1)+y^n-1.

%H G.-N. Han and C. Krattenthaler, <a href="http://arXiv.org/abs/math.RA/0003072">Rectangular Scott-type permanents</a>

%K sign

%O 1,1

%A _Ralf Stephan_, Mar 02 2005