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%I #14 Jan 17 2022 03:48:26
%S 0,1,6,0,1,0,18,0,1,96,0,36,0,1,0,480,0,60,0,1,2880,0,1440,0,90,0,1,0,
%T 20160,0,3360,0,126,0,1,161280,0,80640,0,6720,0,168,0,1,0,1451520,0,
%U 241920,0,12096,0,216,0,1,14515200,0,7257600,0,604800,0,20160,0,270,0,1
%N Triangular sequence of coefficients of the expansion of p(x,t) = exp(x*t)*(1 + t^2)^2/(t*(1 - t^2)).
%D The Beauty of Fractals, Springer-Verlag, New York, 1986, editors Peitgen and Richter, pages 153
%D Terrell Hill, Statistical Mechanics, Dover, 1987, page 329 ff
%e {0, 1},
%e {6, 0, 1},
%e {0, 18, 0, 1},
%e {96, 0, 36, 0, 1},
%e {0, 480, 0, 60, 0, 1},
%e {2880, 0, 1440, 0, 90, 0, 1},
%e {0, 20160, 0, 3360, 0, 126, 0, 1},
%e {161280, 0, 80640, 0, 6720, 0, 168, 0, 1},
%e {0, 1451520, 0, 241920, 0, 12096, 0, 216, 0, 1},
%e {14515200, 0, 7257600, 0, 604800, 0, 20160, 0, 270, 0, 1},
%e {0, 159667200, 0, 26611200, 0, 1330560, 0, 31680, 0, 330, 0, 1}
%t p[t_] = Exp[x*t]*(1 + t^2)^2/(t*(1 - t^2));
%t Table[ ExpandAll[(n + 1)!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], { n, 0, 10}];
%t a = Table[(n + 1)!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}];
%t Flatten[a]
%Y Cf. A136264.
%K nonn,tabf,uned
%O 1,3
%A _Roger L. Bagula_, Apr 28 2008
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