|
%I #3 Mar 30 2012 17:34:26
%S 0,1,-3,2,5,-15,3,-14,56,-42,4,54,-170,290,-90,5,-264,744,-1350,1000,
%T -165,6,1560,-4116,6174,-7210,2695,-273,7,-10800,27264,-37296,41664,
%U -28420,6160,-420,8,85680,-209520,270864,-260064,223524,-89964,12516,-612,9,-766080,1828800,-2274480,2021760,-1587600
%N A triangular sequence of coefficients from a three level exponential expansion function: f(x,t)=Log(1 + t)*(1 - t)*Exp(x*(t - t^2)).
%C Row sums are:
%C {0, 1, -1, -7, 4, 89, -29, -1163, -1840, 32433, -38897}
%C The idea is that the three exponential levels are:
%C 1) Log(1+t)
%C 2) (1-t)
%C 3) Exp(x*(t-t^2))
%F n! times Coefficients of the polynomial expansion: f(x,t)=Log(1 + t)*(1 - t)*Exp(x*(t - t^2))=Sum[(p(x,n)*t^n/n!,{n,0,Infinity}].
%e {0},
%e {1},
%e {-3, 2},
%e {5, -15, 3},
%e {-14, 56, -42,4},
%e {54, -170, 290, -90, 5},
%e {-264, 744, -1350, 1000, -165, 6},
%e {1560, -4116, 6174, -7210, 2695, -273, 7},
%e {-10800, 27264, -37296, 41664, -28420, 6160, -420, 8},
%e {85680, -209520, 270864, -260064, 223524, -89964, 12516, -612, 9},
%e {-766080, 1828800, -2274480, 2021760, -1587600, 958608, -242340, 23280, -855, 10}
%t Clear[p, g] p[t_] = Log[1 + t]*(1 - t)*Exp[x*(t - t^2)] Table[ ExpandAll[n!SeriesCoefficient[Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[SeriesCoefficient[Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
%K tabl,uned,sign
%O 1,3
%A _Roger L. Bagula_, Apr 18 2008
|
