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%I #1 May 16 2003 03:00:00
%S 1,-9,99,-1344,21875,-416016,9058973,-222298112,6069587661,
%T -182500000000,5991545082831,-213243402387456,8177627877990831,
%U -336138206473129984,14742427642822265625,-687141216745680797696,33916850737339807331257
%N a(n)=(-1)^(n+1)n^n(n+(1/12)(n^2-1)).
%C a(n) is the determinant of the n X n matrix M with M(i,i)=2i-n, M(i.j)=i+j.
%F a(n)=(-1)^(n+1)n^n(n+(1/12)(n^2-1)). a(n)=(-1)^n(n^n-n^(n-1)A002378(n)-n^(n-2)A002415(n)).
%t Table[(-1)^(n + 1)n^n(n + (n^2 - 1)/12), {n, 1, 17}]
%K easy,sign
%O 1,2
%A Mario Catalani (mario.catalani(AT)unito.it), Feb 13 2003
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