OFFSET
1,5
COMMENTS
Row sums:
{1, 1, 4, 24, 168, 1560, 17280, 221760, 3265920, 54069120, 994291200}
Row_sum(n)/n!=A000073
REFERENCES
Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 149-150
FORMULA
Coefficients expansion of p(x,n) in f(x,t)=1/(1-t-t^2-t^3)^x=Sum[p(x,n)*t^n/n!m{n,1,Infinity}].
EXAMPLE
{1},
{0, 1},
{0, 3, 1},
{0, 14, 9, 1},
{0, 66, 83, 18, 1},
{0, 504, 750, 275, 30, 1},
{0, 4680, 7954, 3915, 685, 45, 1},
{0, 51120, 96852, 58324, 13965, 1435, 63, 1}, {0, 660240, 1349676, 933156, 280609, 39480, 2674, 84, 1},
{0, 9717120, 21158064, 16282412, 5781132, 1030449, 95256, 4578, 108, 1},
{0, 160755840, 369056016, 309496500, 124949600, 26688375, 3132633, 204750, 7350, 135, 1}
MATHEMATICA
Clear[p, g]; p[t_] = 1/(1 - t - t^2-t^3)^x; 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
KEYWORD
AUTHOR
Roger L. Bagula, Apr 17 2008
STATUS
approved