Summary: For a given natural number $ s$, we study $ s$-Fibonacci sequences $ F_{sn}$ and the corresponding $ s$-Fibonomial coefficients $ \binom{n}{p}_{F_{s}}=\% \frac{F_{sn}F_{s\left( n-1\right) }\cdots F_{s\left( n-p+1\right) }}{\% F_{s}F_{2s}\cdots F_{ps}}$. We obtain the $ Z$ transform of products of powers of $ s$-Fibonacci sequences. Since the $ s$-Fibonomials are involved in this $ Z$ transform, we obtain from it some new results involving products of sequences of the type $ F_{sn+m}^{k}$ together with $ s$-Fibonomials.

11Y55, 11B39

s-fibonomial coefficients, Z transform