A137387 Triangular sequence from coefficients of the expansion of p(x,t)=Exp[2*x*t]*t/(1 - t).

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

Offset

1,3

Comments

Row sums = A066534.

References

Terrell Hill, Statistical Mechanics, Dover, 1987, page 417

Links

Table of n, a(n) for n=1..45.

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.

Sequence in context: A061799 A076868 A056793 * A137394 A062856 A056371

Adjacent sequences: A137384 A137385 A137386 * A137388 A137389 A137390

Keyword

nonn,tabl

Author

Roger L. Bagula, Apr 26 2008

Status

approved