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 A137784 Triangular sequence of coefficients of p(x,t) = t*exp(3*x*t - t^2)/(exp(t) - 1). 0
 2, -3, 18, -44, -72, 216, 360, -1980, -1620, 3240, 7176, 25920, -71280, -38880, 58320, -151200, 753480, 1360800, -2494800, -1020600, 1224720, -3587520, -21772800, 54250560, 65318400, -89812800, -29393280, 29393280, 152409600, -678041280, -2057529600, 3417785280, 3086294400 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 87-100. Frederick T. Wall, Chemical Thermodynamics, W. H. Freeman, San Francisco (1965), pp. 282-290. LINKS Table of n, a(n) for n=1..33. EXAMPLE Triangle begins 2; -3, 18; -44, -72, 216; 360, -1980, -1620, 3240; 7176, 25920, -71280, -38880, 58320; -151200, 753480, 1360800, -2494800, -1020600, 1224720; -3587520, -21772800, 54250560, 65318400, -89812800, -29393280, 29393280; ... MATHEMATICA p[t_] = FullSimplify[(t*Exp[x*t]/(Exp[t] - 1))*Exp[2*x*t - t^2]]; Table[ ExpandAll[(n + 2)!*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[(n + 2)!*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a] CROSSREFS Sequence in context: A134850 A163910 A064777 * A053195 A347429 A211867 Adjacent sequences: A137781 A137782 A137783 * A137785 A137786 A137787 KEYWORD tabl,sign AUTHOR Roger L. Bagula, Apr 28 2008 STATUS approved

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Last modified April 16 03:06 EDT 2024. Contains 371696 sequences. (Running on oeis4.)