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

1,1

Comments

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

References

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

Links

Table of n, a(n) for n=1..32.

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

Example

a(1) = Determinant(A) = 2! = 2.

Maple

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

Prog

(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

Crossrefs

Cf. A111490, A158040-A158044.

Sequence in context: A359006 A097563 A360643 * A157304 A157305 A306416

Adjacent sequences: A158042 A158043 A158044 * A158046 A158047 A158048

Keyword

nonn

Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Extensions

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

Status

approved