A158040 -id:A158040 - cp's OEIS frontend

A158048 Determinant of power series with alternate signs of gamma matrix with determinant 5!.

120, -3120, 1657560, -462870720, 94034430600, -34709926327440, 7736751469771080, -2418878906762872320, 634745166256592831640, -175970074271706846159600, 49274372699370917797432920

Offset: 0

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

sign

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.

			a(1) = Determinant(A) = 5! = 120.

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

Cf. A111490, A158040-A158047.

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

A158049 Determinant of power series with alternate signs of gamma matrix with determinant 6!.

Original entry on oeis.org

720, 95760, 323885520, 520091041680, 646101191031120, 1426723480107570960, 1908953197598354801040, 3574028285578402656777360, 5645446200753726958758372240, 9359837643523957747903959388560

Offset: 0

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..7,1..7) 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) = 6! = 720.

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

Cf. A111490, A158040-A158048.

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

cp's OEIS Frontend

A158048 Determinant of power series with alternate signs of gamma matrix with determinant 5!.

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