A158039 Determinant of power series of gamma matrix with determinant 7!.

5040, 464642640, 9271613897280, 126088436280779280, 1500148651789039497840, 16877281623734016459152640, 186571560637066991905251295920, 2070944486059672103635752020488080

Offset

0,1

Comments

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

where A is the submatrix A(1..8,1..8) 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)!.

References

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

Links

Table of n, a(n) for n=0..7.

Example

a(1) = Determinant(A) = 7! = 5040.

Maple

seq(Determinant(sum(A^i, i=1..n)), n=1..20);

Crossrefs

Cf. A111490, A158040-A158050.

Sequence in context: A010800 A172544 A287083 * A071549 A181752 A208193

Adjacent sequences: A158036 A158037 A158038 * A158040 A158041 A158042

Keyword

nonn

Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Status

approved