A158046 -id:A158046 - cp's OEIS frontend

A158047 Determinant of power series with alternate signs of gamma matrix with determinant 4!.

24, 144, 13896, 842400, 36604920, 2333944368, 126441557448, 6680853691200, 387982670513688, 20676854461594320, 1158249535425969384, 63778918790403180000, 3507499386329443453752, 194248225087593045241968

Offset: 0

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Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

nonn

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)!.

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

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

Cf. A111490, A158040-A158046.

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

cp's OEIS Frontend

A158047 Determinant of power series with alternate signs of gamma matrix with determinant 4!.

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