  It is shown in this note that non-central Stirling numbers s(n,k,a) of the
first kind naturally appear in the expansion of derivatives of the product of a
power function and a logarithn function. We first obtain a recurrence relation
for these numbers, and then, using Leibnitz rule we obtain an explicit formula
for these numbers. We also obtain an explicit formula for s(n,1,a), and then
derive several combinatorial identities related to these numbers.
