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 A137455 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)). 0
 0, 1, -3, 2, 5, -15, 3, -14, 56, -42, 4, 54, -170, 290, -90, 5, -264, 744, -1350, 1000, -165, 6, 1560, -4116, 6174, -7210, 2695, -273, 7, -10800, 27264, -37296, 41664, -28420, 6160, -420, 8, 85680, -209520, 270864, -260064, 223524, -89964, 12516, -612, 9, -766080, 1828800, -2274480, 2021760, -1587600 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums are: {0, 1, -1, -7, 4, 89, -29, -1163, -1840, 32433, -38897} The idea is that the three exponential levels are: 1) Log(1+t) 2) (1-t) 3) Exp(x*(t-t^2)) LINKS FORMULA 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}]. EXAMPLE {0}, {1}, {-3, 2}, {5, -15, 3}, {-14, 56, -42,4}, {54, -170, 290, -90, 5}, {-264, 744, -1350, 1000, -165, 6}, {1560, -4116, 6174, -7210, 2695, -273, 7}, {-10800, 27264, -37296, 41664, -28420, 6160, -420, 8}, {85680, -209520, 270864, -260064, 223524, -89964, 12516, -612, 9}, {-766080, 1828800, -2274480, 2021760, -1587600, 958608, -242340, 23280, -855, 10} MATHEMATICA 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] CROSSREFS Sequence in context: A265759 A057674 A092935 * A111273 A068553 A174909 Adjacent sequences:  A137452 A137453 A137454 * A137456 A137457 A137458 KEYWORD tabl,uned,sign AUTHOR Roger L. Bagula, Apr 18 2008 STATUS approved

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Last modified May 29 04:33 EDT 2020. Contains 334697 sequences. (Running on oeis4.)