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A158048 Determinant of power series with alternate signs of gamma matrix with determinant 5!. 1
120, -3120, 1657560, -462870720, 94034430600, -34709926327440, 7736751469771080, -2418878906762872320, 634745166256592831640, -175970074271706846159600, 49274372699370917797432920 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)