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 A137862 Triangular sequence of coefficients of the expansion of a degenerate partition of Chebyshev U(x,n);A053117 and Hermite H(x,n);A060821 functions: 1) f(x,t)=1/(1-2*x*t+t^2); 2) g(x,t)=Exp[2*x*t-t^2]; to give: p(x,t)=Exp[2*x*t-t^2]/(1-2*x*t+t^2). 0
 1, 0, 4, -4, 0, 20, 0, -60, 0, 128, 60, 0, -768, 0, 1040, 0, 1920, 0, -10400, 0, 10432, -1920, 0, 46800, 0, -156480, 0, 125248, 0, -109200, 0, 1095360, 0, -2630208, 0, 1753600, 109200, 0, -4381440, 0, 26302080, 0, -49100800, 0, 28057856, 0, 9858240, 0, -157812480, 0, 662860800, 0, -1010082816, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums are: {1, 4, 16, 68, 332, 1952, 13648, 109552, 986896, 9865664, 108500864}; LINKS FORMULA p(x,t)=Exp[2*x*t-t^2]/(1-2*x*t+t^2)=Sum(P(x,n)*t^n/n!,{n,0,Infinity}); out_n,m=n!*Coefficients(P(x,n)). EXAMPLE {1}, {0, 4}, {-4, 0, 20}, {0, -60, 0, 128}, {60, 0, -768, 0,1040}, {0, 1920, 0, -10400, 0, 10432}, {-1920, 0, 46800, 0, -156480, 0, 125248}, {0, -109200, 0, 1095360, 0, -2630208, 0, 1753600}, {109200, 0, -4381440, 0, 26302080, 0, -49100800, 0, 28057856}, {0, 9858240, 0, -157812480, 0, 662860800, 0, -1010082816, 0, 505041920}, {-9858240, 0, 591796800, 0, -5523840000, 0, 17676449280, 0, -22726886400, 0, 10100839424} MATHEMATICA Clear[p, b, a]; p[t_] = FullSimplify[(1/(1 - 2*x*t + t^2))*Exp[2*x*t - t^2]]; Table[ ExpandAll[n!*SeriesCoefficient[Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a] CROSSREFS Cf. A060821, A053117. Sequence in context: A121547 A028626 A205507 * A006805 A030045 A126089 Adjacent sequences:  A137859 A137860 A137861 * A137863 A137864 A137865 KEYWORD tabl,uned,sign AUTHOR Roger L. Bagula, Apr 29 2008 STATUS approved

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Last modified September 27 10:35 EDT 2020. Contains 337380 sequences. (Running on oeis4.)