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A158045 Determinant of power series with alternate signs of gamma matrix with determinant 2!. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A308506 A255162 A097563 * 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

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Last modified October 22 12:05 EDT 2021. Contains 348168 sequences. (Running on oeis4.)