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MathGroup Archive 2001

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what are these polynomials called?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26635] what are these polynomials called?
  • From: wouter.meeussen at vandemoortele.com (Wouter Meeussen)
  • Date: Sat, 13 Jan 2001 22:36:13 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Table[(p+1)! CoefficientList[ Sum[k^p,{k,0,n}]/n ,n] ,{p,12}]

produces:

{1, 1}
{1, 3, 2}
{0, 6, 12, 6}
{-4, 0, 40, 60, 24}
{0, -60, 0, 300, 360, 120}
{120, 0, -840, 0, 2520, 2520, 720}
{0, 3360, 0, -11760, 0, 23520, 20160, 5040}
{-12096, 0, 80640, 0, -169344, 0, 241920, 181440, 40320}
{0, -544320, 0, 1814400, 0, -2540160, 0, 2721600, 1814400, 362880}

the row-sums are the factorials, the last element is the next
factorial. It is probably something well-known in thin disguise.

Wouter.


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