|
|
A137785
|
|
Triangular sequence of coefficients of the expansion of p(x,t) = exp(x*t)*(1 + t^2)^2/(t*(1 - t^2)).
|
|
0
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
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
|
|
LINKS
|
|
|
EXAMPLE
|
{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}
|
|
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]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf,uned
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|