ON SOME NEW IDENTITIES FOR THE FIBONOMIAL COEFFICIENTS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F14%3A50002482" target="_blank" >RIV/62690094:18470/14:50002482 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.2478/s12175-014-0241-7" target="_blank" >http://dx.doi.org/10.2478/s12175-014-0241-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2478/s12175-014-0241-7" target="_blank" >10.2478/s12175-014-0241-7</a>

Result language
angličtina
Original language name
ON SOME NEW IDENTITIES FOR THE FIBONOMIAL COEFFICIENTS
Original language description
Let Fn be the nth Fibonacci number. The Fibonomial coefficients ${nbrack k}_F$ are defined for $ngeq k>0$ as follows [{nbrack k}_F=frac{F_n F_{n-1}cdots F_{n-k+1}}{F_1 F_2cdots F_{k}}~, ] with ${nbrack 0}_F=1$ and ${nbrack k}_F=0$ for $n{k$.In this paper, we shall provide several identities among Fibonomial coefficients. In particular, we prove that [ sum_{j=0}^{4l+1} mbox{textrm{sgn}} (2l-j) , {4l+1brack j}_F , F_{n-j} = - frac{F_{2l-1}}{F_{4l+1}} {4l+1brack 2l}_F , F_{n-4l-1},] holds for all non-negative integers $n$ and $l$. %The Fibonomial coefficients belong among generalized %binomial coefficients which was published firstly in 1915 by Fonten'e (see %cite{Fo}) and independently in 1936 by Ward (see cite{Wa}).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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