A158045 Determinant of power series with alternate signs of gamma matrix with determinant 2!.

2, 0, 26, 0, 502, 0, 10306, 0, 213902, 0, 4448666, 0, 92558182, 0, 1925894386, 0, 40073418302, 0, 833837682506, 0, 17350295562262, 0, 361020847688866, 0, 7512036585662702, 0, 156308684773943546, 0, 3252434233373292742, 0, 67675884159595889746, 0

Offset: 1

Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Keywords

• nonn

Comments

a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n), where A is the submatrix A(1..3,1..3) 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) = 2! = 2.
		

References

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

Crossrefs

Cf. A111490, A158040-A158044.

Programs

Maple

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

PARI

vector(100, n, matdet(sum(k=1, n, [1,1,1 ; 1,2,1 ; 1,2,3]^k*(-1)^(k-1)))) \\ Colin Barker, Jul 13 2014

Formula

Empirical g.f.: -2*x*(2*x^2 -1)*(4*x^4 -11*x^2 +1) / ((x -1)*(x +1)*(2*x -1)*(2*x +1)*(2*x^2 -5*x +1)*(2*x^2 +5*x +1)). - Colin Barker, Jul 13 2014

Extensions

More terms, and offset changed to 1 by Colin Barker, Jul 13 2014