Open AccessBinomial Coefficients and Triangular Numbers
Author(s) -
Kantaphon Kuhapatanakul,
A. G. Shan
Publication year - 2021
Publication title -
european journal of mathematics and statistics
Language(s) - English
Resource type - Journals
ISSN - 2736-5484
DOI - 10.24018/ejmath.2021.2.3.31
Subject(s) - binomial coefficient , identity (music) , mathematics , binomial (polynomial) , zhàng , product (mathematics) , gaussian binomial coefficient , binomial distribution , negative binomial distribution , binomial theorem , multinomial distribution , combinatorics , discrete mathematics , statistics , geometry , law , physics , political science , acoustics , china , poisson distribution
We produce formulas of sums the product of the binomial coefficients and triangular numbers. And we apply our formula to prove an identity of Wang and Zhang. Further, we provide an analogue of our identity for the alternating sums.