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%I #16 Nov 27 2015 00:34:52
%S 2,0,26,0,502,0,10306,0,213902,0,4448666,0,92558182,0,1925894386,0,
%T 40073418302,0,833837682506,0,17350295562262,0,361020847688866,0,
%U 7512036585662702,0,156308684773943546,0,3252434233373292742,0,67675884159595889746,0
%N Determinant of power series with alternate signs of gamma matrix with determinant 2!.
%C 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
%C 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)!.
%D G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008.
%F 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
%e a(1) = Determinant(A) = 2! = 2.
%p seq(Determinant(sum(A^i*(-1)^(i-1),i=1..n)), n=1..30);
%o (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
%Y Cf. A111490, A158040-A158044.
%K nonn
%O 1,1
%A _Giorgio Balzarotti_ & _Paolo P. Lava_, Mar 11 2009
%E More terms, and offset changed to 1 by _Colin Barker_, Jul 13 2014
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