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 A158045 Determinant of power series with alternate signs of gamma matrix with determinant 2!. 1
 2, 0, 26, 0, 502, 0, 10306, 0, 213902, 0, 4448666, 0, 92558182, 0, 1925894386, 0, 40073418302, 0, 833837682506, 0, 17350295562262, 0, 361020847688866, 0, 7512036585662702, 0, 156308684773943546, 0, 3252434233373292742, 0, 67675884159595889746, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n), where A is the submatrix A(1..3,1..3) 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)!. REFERENCES G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008. LINKS Table of n, a(n) for n=1..32. FORMULA Empirical g.f.: -2*x*(2*x^2 -1)*(4*x^4 -11*x^2 +1) / ((x -1)*(x +1)*(2*x -1)*(2*x +1)*(2*x^2 -5*x +1)*(2*x^2 +5*x +1)). - Colin Barker, Jul 13 2014 EXAMPLE a(1) = Determinant(A) = 2! = 2. MAPLE seq(Determinant(sum(A^i*(-1)^(i-1), i=1..n)), n=1..30); PROG (PARI) vector(100, n, matdet(sum(k=1, n, [1, 1, 1 ; 1, 2, 1 ; 1, 2, 3]^k*(-1)^(k-1)))) \\ Colin Barker, Jul 13 2014 CROSSREFS Cf. A111490, A158040-A158044. Sequence in context: A359006 A097563 A360643 * A157304 A157305 A306416 Adjacent sequences: A158042 A158043 A158044 * A158046 A158047 A158048 KEYWORD nonn AUTHOR Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009 EXTENSIONS More terms, and offset changed to 1 by Colin Barker, Jul 13 2014 STATUS approved

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Last modified September 12 17:49 EDT 2024. Contains 375853 sequences. (Running on oeis4.)