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%I #11 Feb 04 2023 09:46:21
%S 2,3,0,10,-48,168,3456,-29376,-178560,0,2995200,0,-45158400,
%T 1045094400,-14636482560,-122918584320,-370845941760,12983695441920,
%U -1545691830681600,-62521904633610240,785989658251100160,-2445553599452282880
%N Determinant of the upper left n X n elements excluding its first row and column of the Array T(n,m) in A109626.
%C a(n)=0 for n's, (one less than those in A111605): 3, 10, 12, 28, 30, 33, 34, 35, 36, 37, 38, 40, 42, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 74, 75, 76, 77, 78, 79
%t f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 32}]]; g[n_, m_] := f[n][[m]]; Table[ Det[ Table[ g[i, j], {i, 2, n}, {j, 2, n}]]{n, 23}]
%Y Cf. A109626, A111605.
%K sign
%O 1,1
%A _Paul D. Hanna_ and _Robert G. Wilson v_, Aug 01 2005
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