On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials

In this paper, we consider and obtain binomial sums and alternating binomial sums including falling factorial of the summation indices. For example, for nonnegative integer $m,$ \begin{eqnarray*} &&\sum\limits_{k=0}^{n}\dbinom{n}{k}k^{\underline{m}}U_{2k}^{2m}=\frac{n^{\underline{m}}}{\left( p^{2}+4\right) ^{m}}\left( \sum\limits_{i=0}^{m}\left( -1\right) ^{i}\dbinom{2m}{i}V_{2\left( m-i\right) }^{n-m}V_{2\left( m+n\right) \left( m-i\right) }-\left( -1\right) ^{m}2^{n-m}\dbinom{2m}{m}\right),

Keywords:

Generalized Fibonacci numbers sums, falling factorials,

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Mathematical Sciences and Applications E-Notes-Cover

ISSN: 2147-6268
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: -

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