A111605 Determinant of the upper left n X n elements of the array T(n, m) in A109626.

1, 1, 2, 2, 8, -40, 144, 2448, -17280, -71424, 0, 1198080, 0, -18063360, 418037760, -7498137600, -115688079360, -587977850880, 12300343050240, -540240522117120, -36548032147292160, 487948583538524160, -2339225182084792320

Offset: 1

Author

Paul D. Hanna and Robert G. Wilson v, Aug 01 2005

Keywords

• sign

Comments

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

Crossrefs

Cf. A109626, A111606.

Programs

Mathematica

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}]