PowerSum coefficients in symbolic form.
$\displaystyle a_{k+1} = \frac{1}{k+1}$
$\displaystyle a_k=\frac{1}{2}$
$\displaystyle a_{k-1}=\frac{k}{12}$
$\displaystyle a_{k-2} = 0$
$\displaystyle a_{k-3} = \frac{k(k-1)(k-2)}{720}$
$\displaystyle a_{k-4} = 0$
$\displaystyle a_{k-5} = \frac{k(k-1)(k-2)(k-3)(k-4)}{30240}$
$\displaystyle a_{k-6} = 0$
$\displaystyle a_{k-7} = -\frac{k(k-1)(k-2)(k-3)(k-4)(k-5)(k-6)}{1209600}$
$\displaystyle a_{k-8} = 0$
$\displaystyle a_{k-9} = \frac{\prod_{i=0}^{8} (k-i)}{47900160}$
$\displaystyle a_{k-10} = 0$
$\displaystyle a_{k-11} = -\frac{691 \prod_{i=0}^{10} (k-i)}{1307674368000}$
$\displaystyle a_{k-12} = 0$
$\displaystyle a_{k-13} = \frac{\prod_{i=0}^{12} (k-i)}{74724249600}$
$\displaystyle a_{k-14} = 0$
$\displaystyle a_{k-15} = -\frac{3617 \prod_{i=0}^{14} (k-i)}{10670622842880000}$
$\displaystyle a_{k-16} = 0$
$\displaystyle a_{k-17} = \frac{43867 \prod_{i=0}^{16} (k-i)}{5109094217170944000}$
$\displaystyle a_{k-18} = 0$
$\displaystyle a_{k-19} = -\frac{174611 \prod_{i=0}^{18} (k-i)}{802857662698291200000}$
$\displaystyle a_{k-20} = 0$
$\displaystyle a_{k-21} = \frac{77683 \prod_{i=0}^{20} (k-i)}{14101100039391805440000}$
$\displaystyle a_{k-22} = 0$
$\displaystyle a_{k-23} = -\frac{236364091 \prod_{i=0}^{22} (k-i)}{1693824136731743669452800000}$
$\displaystyle a_{k-24} = 0$
