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Triangle: p(x) = (1 - t/c)*(1 - t)^(-x - b); c = 1/2; b = 1.
0

%I #10 Feb 18 2024 04:08:58

%S 1,-1,1,-2,-1,1,-6,-7,0,1,-24,-38,-13,2,1,-120,-226,-125,-15,5,1,-720,

%T -1524,-1076,-285,-5,9,1,-5040,-11628,-9604,-3521,-490,28,14,1,-40320,

%U -99504,-91988,-41020,-8911,-616,98,20,1,-362880,-945936,-953532,-487432,-134757,-18375,-378,222,27,1,-3628800

%N Triangle: p(x) = (1 - t/c)*(1 - t)^(-x - b); c = 1/2; b = 1.

%e {1},

%e {-1, 1},

%e {-2, -1, 1},

%e {-6, -7, 0, 1},

%e {-24, -38, -13, 2, 1},

%e {-120, -226, -125, -15, 5, 1},

%e {-720, -1524, -1076, -285, -5, 9, 1},

%e {-5040, -11628, -9604, -3521, -490,28, 14, 1},

%e {-40320, -99504, -91988, -41020, -8911, -616, 98, 20,1},

%e {-362880, -945936, -953532, -487432, -134757, -18375, -378,222, 27, 1},

%e ...

%t c = 1/2; b = 1;

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

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

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

%t Flatten[a]

%K uned,tabl,sign,less

%O 1,4

%A _Roger L. Bagula_, Apr 09 2008