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

Original entry on oeis.org

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

Examples

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

References

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

Crossrefs

Cf. A111490, A158040-A158047.

Programs

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