A158050 - OEIS

%I #10 Nov 27 2015 00:30:50

%S 5040,-4137840,99515142720,-1122871063189680,9688118420572305840,

%T -150299359081533202947840,1405831144255746621131643120,

%U -18442639987146150894175704882480,203561673763315319923663885655833920

%N Determinant of power series with alternate signs of gamma matrix with determinant 7!.

%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..8,1..8) 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) = 7! = 5040.

%p seq(Determinant(sum(A^i*(-1)^(i-1),i=1..n)),n=1..20);

%Y Cf. A111490, A158040-A158049.

%K sign

%O 0,1

%A _Giorgio Balzarotti_ & _Paolo P. Lava_, Mar 11 2009