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Coefficients of expansion polynomial:p(x,t)=Exp[ -t^2* x](1 - t)^(-x)/x
0

%I #2 Mar 30 2012 17:34:39

%S 1,-1,1,2,-3,1,6,11,-6,1,24,10,35,-10,1,120,94,-45,85,-15,1,720,756,

%T 364,-315,175,-21,1,5040,6348,2828,1729,-1120,322,-28,1,40320,57744,

%U 27404,5796,7329,-3024,546,-36,1,362880,572976,298980,81080,-4725,25473,-6930

%N Coefficients of expansion polynomial:p(x,t)=Exp[ -t^2* x](1 - t)^(-x)/x

%C Row sums are:

%C {1, 0, 0, 12, 60, 240, 1680, 15120, 136080, 1330560,...}

%F p(x,t)=Exp[ -t^2* x](1 - t)^(-x)/x

%e {1},

%e {-1, 1},

%e {2, -3, 1},

%e {6, 11, -6, 1},

%e {24, 10, 35, -10, 1},

%e {120, 94, -45, 85, -15, 1},

%e {720, 756, 364, -315, 175, -21, 1},

%e {5040, 6348, 2828, 1729, -1120, 322, -28, 1},

%e {40320, 57744, 27404, 5796, 7329, -3024, 546, -36, 1},

%e {362880, 572976, 298980, 81080, -4725, 25473, -6930, 870, -45, 1}

%t p[t_] = Exp[ -t^2* x](1 - t)^(-x)/x;

%t Table[ ExpandAll[n!SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 1, 10}];

%t a = Table[n! CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 1, 10}];

%t Flatten[a]

%K sign,tabl,uned

%O 1,4

%A _Roger L. Bagula_, Apr 01 2010