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%I #16 Nov 27 2015 00:32:01
%S 6,372,8862,148800,2096886,26922756,332847654,4138425600,53260806102,
%T 715168132932,9918365312598,139707565435200,1971543518031366,
%U 27670255890476676,385457279875640742,5335884957031756800,73579514340980051958,1013129779240735463748
%N Determinant of power series of gamma matrix with determinant 3!.
%C a(n) = Determinant(A + A^2 + A^3 + A^4 + A^5 + ... + A^n) where A is the submatrix A(1..4,1..4) 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)!.
%D G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008.
%F Empirical g.f.: -6*x*(6*x^2 -1)*(46656*x^12 -828144*x^10 +2517696*x^9 -3533544*x^8 +2852496*x^7 -1444952*x^6 +475416*x^5 -98154*x^4 +11656*x^3 -639*x^2 +1) / ((x -1)*(6*x -1)*(6*x^4 -22*x^3 +23*x^2 -10*x +1)*(216*x^4 -360*x^3 +138*x^2 -22*x +1)*(216*x^6 -828*x^5 +1284*x^4 -808*x^3 +214*x^2 -23*x +1)). - _Colin Barker_, Jul 13 2014
%e a(1) = Determinant(A) = 3! = 6.
%p with(LinearAlgebra):
%p A:= <<1|1|1|1>, <1|2|1|2>, <1|2|3|1>, <1|2|3|4>>:
%p seq(Determinant(add(A^i, i=1..n)), n=1..30);
%o (PARI) vector(100, n, matdet(sum(k=1, n, [1,1,1,1 ; 1,2,1,2 ; 1,2,3,1 ; 1,2,3,4]^k))) \\ _Colin Barker_, Jul 13 2014
%Y Cf. A111490, A158040.
%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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