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

Authors : Sibel KOPARAL, Neşe ÖMÜR

Pages : 123-129

Doi:10.36753/mathenot.708004

View : 44 | Download : 7

Publication Date : 2020-10-15

Article Type : Research Paper

Abstract :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}}}{\leftinsert ignore into journalissuearticles values( p^{2}+4\right); ^{m}}\leftinsert ignore into journalissuearticles values( \sum\limits_{i=0}^{m}\leftinsert ignore into journalissuearticles values( -1\right); ^{i}\dbinom{2m}{i}V_{2\leftinsert ignore into journalissuearticles values( m-i\right); }^{n-m}V_{2\leftinsert ignore into journalissuearticles values( m+n\right); \leftinsert ignore into journalissuearticles values( m-i\right); }-\leftinsert ignore into journalissuearticles values( -1\right); ^{m}2^{n-m}\dbinom{2m}{m}\right);,
Keywords : Generalized Fibonacci numbers, sums, falling factorials

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