We will concentrate on special types of numbers
Jn
(k) =
n−2
Xi
=0
ni kn−2−i,
where k is any nonnegative integer and n is any positive integer greater than 1.
These numbers are a generalization of generalized repunits Rn(b). In this paper
some results about divisibility of Jn(k) are stated. Further the generating
function and a m-fold convolution formula for the numbers J
n(k) is found.