A158043 Determinant of power series of gamma matrix with determinant 5!.

120, 207600, 96647880, 30798705600, 8636938282920, 2309545097941200, 608543327609001240, 160948481103837273600, 43112754053898172364280, 11708778018848186302158000, 3213002829193456223967295560

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 submatrix A(1..6,1..6) 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) = 5! = 120.
		

References

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

Crossrefs

Cf. A111490, A158040, A158041, A158042.

Programs

Maple

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