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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A158050 Determinant of power series with alternate signs of gamma matrix with determinant 7!.

Original entry on oeis.org

5040, -4137840, 99515142720, -1122871063189680, 9688118420572305840, -150299359081533202947840, 1405831144255746621131643120, -18442639987146150894175704882480, 203561673763315319923663885655833920
Offset: 0

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Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Keywords

Comments

a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n)
where A is the submatrix A(1..8,1..8) 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.

Examples

			a(1) = Determinant(A) = 7! = 5040.

References

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

Crossrefs

Cf. A111490, A158040-A158049.

Programs

  • Maple
    seq(Determinant(sum(A^i*(-1)^(i-1),i=1..n)),n=1..20);
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