A158044 Determinant of power series of gamma matrix with determinant 6!.

720, 8482320, 23846746320, 46069117007760, 78423934939027920, 126377664053739048720, 199725313669091369807760, 316583663401497456387173520, 508625335390476191389947899280

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..7,1..7) 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) = 6! = 720.
		

References

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

Crossrefs

Cf. A111490, A158040, A158041, A158042, A158043.

Programs

Maple

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