S000686


The n+1 degree polynomial which computes A064538(n) times the sum of the n-th powers of positive integers (constant term last).

1, 0, 1, 1, 0, 2, 3, 1, 0, 1, 2, 1, 0, 0, 6, 15, 10, 0, -1, 0, 2, 6, 5, 0, -1, 0, 0, 6, 21, 21, 0, -7, 0, 1, 0, 3, 12, 14, 0, -7, 0, 2, 0, 0, 10, 45, 60, 0, -42, 0, 20, 0, -3, 0, 2, 10, 15, 0, -14, 0, 10, 0, -3, 0, 0, 6, 33, 55, 0, -66, 0, 66, 0, -33, 0, 5, 0, 2

0

S000686

A negative term x is plotted as -Log10(-x).

T. D. Noe, Plot of 101 rows

T. D. Noe, Table of 101 rows

(Mma) Table[s = (Sum[(-1)^k Binomial[p + 1, k] BernoulliB[k] n^(p + 1 - k), {k, 0, p}])/(p + 1); d = Denominator[f = Factor[s]]; Reverse[CoefficientList[Expand[d*s], n]], {p, 0, 10}]

Cf. A064538, S000685.

nonn,tabl

T. D. Noe, Jul 14 2015

© Tony D Noe 2014-2015