A158048 Determinant of power series with alternate signs of gamma matrix with determinant 5!.

120, -3120, 1657560, -462870720, 94034430600, -34709926327440, 7736751469771080, -2418878906762872320, 634745166256592831640, -175970074271706846159600, 49274372699370917797432920

Offset

0,1

Comments

a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*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)!.

a(n) is even with respect to signs of power of A.

References

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

Links

Table of n, a(n) for n=0..10.

Example

a(1) = Determinant(A) = 5! = 120.

Maple

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

Crossrefs

Cf. A111490, A158040-A158047.

Sequence in context: A250651 A052721 A060490 * A219477 A183266 A231129

Adjacent sequences: A158045 A158046 A158047 * A158049 A158050 A158051

Keyword

sign

Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Status

approved