On some identities for the Fibonomial coefficients

Rok, strany: 2005, 9 - 19

The Fibonomial coefficients $[smallmatrix n\kendsmallmatrix]$ are defined for positive integers $n≥ k$ as follows

$$ matrix n k endbmatrix =((F_n F_n-1… F_n-k+1) / (F₁ F₂ … F_k)) , $$

with $[smallmatrix n\0 endsmallmatrix]=1$, where the Fibonacci numbers are given by the recurrence relation $F_n+2=F_n+1+F_n$, $F₀=0$, $F₁=1$. In this paper new identities for the Fibonomial coefficients are derived. These identities are related to the generating function of the $k$ th powers of the Fibonacci numbers. Their proofs are based on a reasonable manipulation with these generating functions.

ISO 690:

Seibert, J., Trojovský, P. 2005. On some identities for the Fibonomial coefficients. In Mathematica Slovaca, vol. 55, no.1, pp. 9-19. 0139-9918.

APA:

Seibert, J., Trojovský, P. (2005). On some identities for the Fibonomial coefficients. Mathematica Slovaca, 55(1), 9-19. 0139-9918.