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A215065 Triangle read by rows, e.g.f. exp(x*z)/((exp(x/2)+exp(x*3/2))/((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3)-1).

%I A215065 #12 Jul 29 2013 08:34:31
%S A215065 1,-1,1,1,-2,1,1,3,-3,1,-11,4,6,-4,1,49,-55,10,10,-5,1,-137,294,-165,
%T A215065 20,15,-6,1,-127,-959,1029,-385,35,21,-7,1,5573,-1016,-3836,2744,-770,
%U A215065 56,28,-8,1,-50399,50157,-4572,-11508,6174,-1386,84
%N A215065 Triangle read by rows, e.g.f. exp(x*z)/((exp(x/2)+exp(x*3/2))/((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3)-1).
%C A215065 Matrix inverse is A215064.
%e A215065 [0] [1]
%e A215065 [1] [-1, 1]
%e A215065 [2] [1, -2, 1]
%e A215065 [3] [1, 3, -3, 1]
%e A215065 [4] [-11, 4, 6, -4, 1]
%e A215065 [5] [49, -55, 10, 10, -5, 1]
%e A215065 [6] [-137, 294, -165, 20, 15, -6, 1]
%e A215065 [7] [-127, -959, 1029, -385, 35, 21, -7, 1]
%e A215065 [8] [5573, -1016, -3836, 2744, -770, 56, 28, -8, 1]
%e A215065 [9] [-50399, 50157, -4572, -11508, 6174, -1386, 84, 36, -9, 1]
%t A215065 max = 10; f = Exp[x*z]/((Exp[x/2] + Exp[x*(3/2)])/((Exp[3*(x/2)] + 2*Cos[Sqrt[3]*(x/2)])/3) - 1); coes = CoefficientList[ Series[f, {x, 0, max}, {z, 0, max}], {x, z}]; Table[ coes[[n, k]]*(n - 1)!, {n, 1, max}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jul 29 2013 *)
%o A215065 (Sage)
%o A215065 def A215065_triangle(dim): # See A215060 for function 'triangle'.
%o A215065     var('x, z')
%o A215065     f = exp(x*z)/((exp(x/2)+exp(x*3/2))/((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3)-1)
%o A215065     return triangle(f, dim)
%o A215065 A215065_triangle(12)
%Y A215065 Cf. A215060, A215061, A215062, A215063, A215064.
%K A215065 sign,tabl
%O A215065 0,5
%A A215065 _Peter Luschny_, Aug 01 2012