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%I #18 Feb 14 2015 10:56:18
%S -1,1,-1,3,-3,1,1,4,2,-8,-5,8,2,-4,1,-1,-5,-15,-25,-25,-1,25,35,5,-15,
%T -21,5,5,5,-5,1,1,6,21,56,114,186,246,246,171,34,-114,-174,-149,-54,
%U 54,66,51,6,-34,-6,-6,4,9,-6,1,-1,-7,-28,-84,-210,-448,-833,-1373,-2023,-2653,-3094,-3178,-2793,-1953,-883,161,917,1197
%N Irregular triangle read by rows: coefficients of Olinde Rodrigues recursive polynomial for inversions of permutations applied to Bonnaci type polynomials: x - 1, x^2 - x - 1, x^3 - x^2 - x - 1, etc.
%C The polynomial powers grow as I(n) = n!*binomial(n,2)/2.
%H Warren P. Johnson, <a href="http://www.jstor.org/stable/27642326">Mathematics and Social Utopias in France: Olinde Rodrigues and His times by Simon Altmann; Eduardo L. Ortiz</a>, American Math. Monthly, Oct 2007, volume 114, number 8, pages 752-758.
%e {-1},
%e {1},
%e {-1, 3, -3, 1},
%e {1, 4, 2, -8, -5, 8, 2, -4, 1},
%e {-1, -5, -15, -25, -25, -1, 25, 35, 5, -15, -21, 5, 5, 5, -5, 1},
%e {1, 6, 21, 56, 114, 186, 246, 246, 171, 34, -114, -174, -149, -54, 54, 66, 51, 6, -34, -6, -6, 4, 9, -6,1},
%e {-1, -7, -28, -84, -210, -448, -833, -1373, -2023, -2653, -3094, -3178, -2793, -1953, -883, 161, 917, 1197, 987, 567,91, -253, -343, -203, -98, 28, 91, 63, -15, 7, -14, -14, 0, 14, -7, 1},
%t f[q_, n_] = If[n == 0, -1, q^(n - 1) - Sum[q^i, {i, 0, n - 2}]]; g[q_, n_] = Product[f[q, n], {m, 0, n}]; a = Table[CoefficientList[g[x, n], x], {n, 0, 10}]; Flatten[a]
%K uned,sign,tabf
%O 1,4
%A _Roger L. Bagula_, Oct 19 2007