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.