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A158047 Determinant of power series with alternate signs of gamma matrix with determinant 4!. 1
24, 144, 13896, 842400, 36604920, 2333944368, 126441557448, 6680853691200, 387982670513688, 20676854461594320, 1158249535425969384, 63778918790403180000, 3507499386329443453752, 194248225087593045241968 (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..5,1..5) 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..13.

EXAMPLE

a(1) = Determinant(A) = 4! = 24.

MAPLE

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

CROSSREFS

Cf. A111490, A158040-A158046.

Sequence in context: A029572 A129923 A064138 * A042116 A215756 A290313

Adjacent sequences:  A158044 A158045 A158046 * A158048 A158049 A158050

KEYWORD

nonn

AUTHOR

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

STATUS

approved

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Last modified February 19 16:24 EST 2020. Contains 332045 sequences. (Running on oeis4.)