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

#### Sibel KOPARAL [1] , Neşe ÖMÜR [2]

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),
Generalized Fibonacci numbers, sums, falling factorials
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Primary Language en Mathematics Articles Orcid: 0000-0001-9574-9652Author: Sibel KOPARAL (Primary Author)Institution: KOCAELİ ÜNİVERSİTESİCountry: Turkey Orcid: 0000-0002-3972-9910Author: Neşe ÖMÜR Institution: Kocaeli UniversityCountry: Turkey Publication Date : October 15, 2020
 Bibtex @research article { mathenot708004, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2020}, volume = {8}, pages = {123 - 129}, doi = {10.36753/mathenot.708004}, title = {On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials}, key = {cite}, author = {Koparal, Sibel and Ömür, Neşe} } APA Koparal, S , Ömür, N . (2020). On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials . Mathematical Sciences and Applications E-Notes , 8 (2) , 123-129 . DOI: 10.36753/mathenot.708004 MLA Koparal, S , Ömür, N . "On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials" . Mathematical Sciences and Applications E-Notes 8 (2020 ): 123-129 Chicago Koparal, S , Ömür, N . "On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials". Mathematical Sciences and Applications E-Notes 8 (2020 ): 123-129 RIS TY - JOUR T1 - On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials AU - Sibel Koparal , Neşe Ömür Y1 - 2020 PY - 2020 N1 - doi: 10.36753/mathenot.708004 DO - 10.36753/mathenot.708004 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 123 EP - 129 VL - 8 IS - 2 SN - -2147-6268 M3 - doi: 10.36753/mathenot.708004 UR - https://doi.org/10.36753/mathenot.708004 Y2 - 2020 ER - EndNote %0 Mathematical Sciences and Applications E-Notes On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials %A Sibel Koparal , Neşe Ömür %T On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials %D 2020 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 8 %N 2 %R doi: 10.36753/mathenot.708004 %U 10.36753/mathenot.708004 ISNAD Koparal, Sibel , Ömür, Neşe . "On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials". Mathematical Sciences and Applications E-Notes 8 / 2 (October 2020): 123-129 . https://doi.org/10.36753/mathenot.708004 AMA Koparal S , Ömür N . On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials. Math. Sci. Appl. E-Notes. 2020; 8(2): 123-129. Vancouver Koparal S , Ömür N . On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials. Mathematical Sciences and Applications E-Notes. 2020; 8(2): 123-129. IEEE S. Koparal and N. Ömür , "On Binomial Sums and Alternating Binomial Sums of Generelized Fibonacci Numbers with Falling Factorials", Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, pp. 123-129, Oct. 2020, doi:10.36753/mathenot.708004

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