Geodesic
On \(s\)-fibonomials
Journal of integer sequences, Tome 14 (2011) no. 3
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.
Classification : 11Y55, 11B39
Keywords: s-fibonomial coefficients, Z transform 
@article{JIS_2011__14_3_a0,
     author = {de Jes\'us Pita Ruiz Velasco,  Claudio},
     title = {On \(s\)-fibonomials},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {3},
     zbl = {1232.11018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_3_a0/}
}
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de Jesús Pita Ruiz Velasco,  Claudio. On \(s\)-fibonomials. Journal of integer sequences, Tome 14 (2011) no. 3. http://geodesic.mathdoc.fr/item/JIS_2011__14_3_a0/