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 A158050 Determinant of power series with alternate signs of gamma matrix with determinant 7!. 2
 5040, -4137840, 99515142720, -1122871063189680, 9688118420572305840, -150299359081533202947840, 1405831144255746621131643120, -18442639987146150894175704882480, 203561673763315319923663885655833920 (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..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. REFERENCES G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008 LINKS EXAMPLE a(1) = Determinant(A) = 7! = 5040. MAPLE seq(Determinant(sum(A^i*(-1)^(i-1), i=1..n)), n=1..20); CROSSREFS Cf. A111490, A158040-A158049. Sequence in context: A178140 A180369 A053876 * A063411 A008552 A221437 Adjacent sequences:  A158047 A158048 A158049 * A158051 A158052 A158053 KEYWORD sign AUTHOR Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009 STATUS approved

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Last modified January 28 23:12 EST 2022. Contains 350670 sequences. (Running on oeis4.)