A158039 - OEIS

%I #11 Nov 27 2015 00:32:56

%S 5040,464642640,9271613897280,126088436280779280,

%T 1500148651789039497840,16877281623734016459152640,

%U 186571560637066991905251295920,2070944486059672103635752020488080

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

%C a(n) = Determinant(A + A^2 + A^3 + A^4 + A^5 + ... + 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)!.

%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,i=1..n)),n=1..20);

%Y Cf. A111490, A158040-A158050.

%K nonn

%O 0,1

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