A137785 Triangular sequence of coefficients of the expansion of p(x,t) = exp(x*t)*(1 + t^2)^2/(t*(1 - t^2)).

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, 20160, 0, 3360, 0, 126, 0, 1, 161280, 0, 80640, 0, 6720, 0, 168, 0, 1, 0, 1451520, 0, 241920, 0, 12096, 0, 216, 0, 1, 14515200, 0, 7257600, 0, 604800, 0, 20160, 0, 270, 0, 1

Offset: 1

Author

Roger L. Bagula, Apr 28 2008

Keywords

• nonn
• tabf
• uned

Examples

			{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, 20160, 0, 3360, 0, 126, 0, 1},
{161280, 0, 80640, 0, 6720, 0, 168, 0, 1},
{0, 1451520, 0, 241920, 0, 12096, 0, 216, 0, 1},
{14515200, 0, 7257600, 0, 604800, 0, 20160, 0, 270, 0, 1},
{0, 159667200, 0, 26611200, 0, 1330560, 0, 31680, 0, 330, 0, 1}
		

References

• The Beauty of Fractals, Springer-Verlag, New York, 1986, editors Peitgen and Richter, pages 153
• Terrell Hill, Statistical Mechanics, Dover, 1987, page 329 ff

Crossrefs

Cf. A136264.

Programs

Mathematica

p[t_] = Exp[x*t]*(1 + t^2)^2/(t*(1 - t^2));
Table[ ExpandAll[(n + 1)!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], { n, 0, 10}];
a = Table[(n + 1)!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}];
Flatten[a]