A158042 Determinant of power series of gamma matrix with determinant 4!.

24, 7200, 671832, 42120000, 2259461784, 116697218400, 6145075369464, 334042684560000, 18529848376972632, 1033842723079716000, 57545200744624079544, 3188945939520159000000, 176129265145080634433304

Offset: 0

Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Keywords

• nonn

Comments

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

where A is the submtrix A(1..5,1..5) of the matrix with factorial determinant

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)!.

Examples

			a(1) = Determinant(A) = 4! = 24.
		

References

• G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008.

Crossrefs

Cf. A111490, A158040, A158041.

Programs

Maple

seq(Determinant(sum(A^i,i=1..n)),n=1..30);