A137784 Triangular sequence of coefficients of p(x,t) = t*exp(3*x*t - t^2)/(exp(t) - 1).

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

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