|
Search: id:A137387
|
|
|
| A137387 |
|
Triangular sequence from coefficients of the expansion of p(x,t)=Exp[2*x*t]*t/(1 - t). |
|
+0
1
|
|
| 0, 1, 2, 4, 6, 12, 12, 24, 48, 48, 32, 120, 240, 240, 160, 80, 720, 1440, 1440, 960, 480, 192, 5040, 10080, 10080, 6720, 3360, 1344, 448, 40320, 80640, 80640, 53760, 26880, 10752, 3584, 1024, 362880, 725760, 725760, 483840, 241920, 96768, 32256, 9216
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Row sums = A066534.
|
|
REFERENCES
|
Terrell Hill, Statistical Mechanics, Dover, 1987, page 417
|
|
FORMULA
|
p(x,t)=Exp[2*x*t]*t/(1 - t)=Sum[P(x,n)*t6n/n!,{n,1,Infinity}]; out_n,m=n!*Coefficients(P(x,n)).
|
|
EXAMPLE
|
{0},
{1},
{2, 4},
{6, 12, 12},
{24, 48, 48, 32},
{120, 240, 240, 160, 80},
{720, 1440, 1440, 960, 480, 192},
{5040, 10080, 10080, 6720, 3360, 1344, 448},
{40320, 80640, 80640, 53760, 26880, 10752, 3584, 1024},
{362880, 725760, 725760, 483840, 241920, 96768, 32256, 9216, 2304},
{3628800, 7257600, 7257600, 4838400, 2419200, 967680, 322560, 92160, 23040,5120}
|
|
MATHEMATICA
|
p[t_] = Exp[2*x*t]*t/(1 - t); Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
|
|
CROSSREFS
|
Cf. A066534.
Adjacent sequences: A137384 A137385 A137386 this_sequence A137388 A137389 A137390
Sequence in context: A061799 A076868 A056793 this_sequence A137394 A062856 A056371
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 26 2008
|
|
|
Search completed in 0.002 seconds
|
