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%I #9 Feb 04 2023 09:46:34
%S 1,1,2,2,8,-40,144,2448,-17280,-71424,0,1198080,0,-18063360,418037760,
%T -7498137600,-115688079360,-587977850880,12300343050240,
%U -540240522117120,-36548032147292160,487948583538524160,-2339225182084792320
%N Determinant of the upper left n X n elements of the array T(n, m) in A109626.
%C a(n)=0 for n's: 11, 13, 29, 31, 34, 35, 36, 37, 38, 39, 41, 43, 46, 47, 48, 49, 50, 51, 53,59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 77, 78, 79, 80
%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, n}, {j, n}]], {n, 23}]
%Y Cf. A109626, A111606.
%K sign
%O 1,3
%A _Paul D. Hanna_ and _Robert G. Wilson v_, Aug 01 2005
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