  We study the problem of generalization of Oresme numbers with a new sequence
of numbers called Oresme polynomials. Moreover, by using the matrix methods for
Oresme polynomials, we obtain the identities including the general bilinear
index-reduction formula of these numbers. Further, Oresme polynomials that are
natural extensions of the $k$-Oresme numbers are introduced and some relations
for the derivatives of these polynomials in the form of convolution are proved.

Combinatorics