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%I #9 Nov 27 2015 00:36:12
%S 120,-3120,1657560,-462870720,94034430600,-34709926327440,
%T 7736751469771080,-2418878906762872320,634745166256592831640,
%U -175970074271706846159600,49274372699370917797432920
%N Determinant of power series with alternate signs of gamma matrix with determinant 5!.
%C a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n)
%C where A is the submatrix A(1..6,1..6) of the matrix with factorial determinant
%C A = [[1,1,1,1,1,1,...], [1,2,1,2,1,2,...], [1,2,3,1,2,3,...], [1,2,3,4,1,2,...], [1,2,3,4,5,1,...], [1,2,3,4,5,6,...], ...]; note: Determinant A(1..n,1..n) = (n-1)!.
%C a(n) is even with respect to signs of power of A.
%D G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008.
%e a(1) = Determinant(A) = 5! = 120.
%p seq(Determinant(sum(A^i*(-1)^(i-1),i=1..n)),n=1..30);
%Y Cf. A111490, A158040-A158047.
%K sign
%O 0,1
%A _Giorgio Balzarotti_ & _Paolo P. Lava_, Mar 11 2009
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