# On sums related to the numerator of generating functions for the $k$th power of Fibonacci numbers

In: Mathematica Slovaca, vol. 60, no. 6
Pavel Pražák - Pavel Trojovský
Detaily:
Rok, strany: 2010, 751 - 770
Kľúčové slová:
generating function, Riordan's theorem, Generalized Fibonacci numbers, Fibonacci numbers, Lucas numbers
O článku:
New results about some sums $sn(k,l)$ of products of the Lucas numbers, which are of similar type as the sums in [SEIBERT, J.—TROJOVSKÝ, P.: \textit{On multiple sums of products of Lucas numbers}, J. Integer Seq. \textbf{10} (2007), Article 07.4.5], and sums $\sigma(k)=\sum_{l=0}^{\frac{k-1}2}\binom{k}{l}F_{k-2l}s_n(k,l)$ are derived. These sums are related to the numerator of generating function for the $k$th powers of the Fibonacci numbers. $s_n(k,l)$ and $\sigma(k)$ are expressed as the sum of the binomial and the Fibonomial coefficients. Proofs of these formulas are based on a special inverse formulas.
Ako citovať:
ISO 690:
Pražák, P., Trojovský, P. 2010. On sums related to the numerator of generating functions for the $k$th power of Fibonacci numbers. In Mathematica Slovaca, vol. 60, no.6, pp. 751-770. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0044-4

APA:
Pražák, P., Trojovský, P. (2010). On sums related to the numerator of generating functions for the $k$th power of Fibonacci numbers. Mathematica Slovaca, 60(6), 751-770. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0044-4
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