Results 31 to 40 of about 46,123 (300)
Practical numbers among the binomial coefficients [PDF]
, 2020 A practical number is a positive integer n such that every positive integer less than n can be written as a sum of distinct divisors of n. We prove that most of the binomial coefficients are practical numbers. Precisely, letting f(n) denote the number of
Sanna Carlo, Leonetti P, Leonetti Paolo
core +1 more source
Sums of Reciprocals of Triple Binomial Coefficients
International Journal of Mathematics and Mathematical Sciences, 2008 We investigate the integral representation of infinite sums involving the reciprocals of triple binomial coefficients. We also recover some wellknown properties of 𝜁(3) and extend the range of results given by other authors.
A. Sofo
doaj +1 more source
On some series involving the binomial coefficients $binom{3n}{n}$ [PDF]
Notes on Number Theory and Discrete MathematicsUsing a simple transformation, we obtain much simpler forms for some series involving binomial coefficients $binom{3n}{n}$ derived by Necdet Batir. New evaluations are given and connections with Fibonacci numbers and the golden ratio are established ...
Kunle Adegoke +2 more
doaj +1 more source
Binomial coefficients and their visualization [PDF]
, 2019 In this paper, the authors present some of the results achieved by mathematicians who belonged to different cultures and lived in different time periods, but were engaged in determining (formula for determining) binomial coefficients.
Popović, Branislav +3 more
core +1 more source
, 2022 This paper presents a theorem on the binomial coefficients of combinatorial geometric series and its solutions for the binomial expression under the partitions of the binomial coefficients.
Chinnaraji Annamalai
core +1 more source
Ray trajectories, binomial coefficients of a new type, and the binary system [PDF]
Компьютерные исследования и моделирование, 2010 The paper describes a new algorithm of construction of the nonlinear arithmetic triangle on the basis of numerical simulation and the binary system. It demonstrates that the numbers that fill the nonlinear arithmetic triangle may be binomial coefficients
Aleksandr Vladimirovich Yurkin
doaj +1 more source
Tables of binomial coefficients and Stirling numbers
, 1976 Tables of Binomial coefficients and of Stirling numbers are given, along with the most important formulas and relationships satisfied by them.
Goldberg, Karl; Leighton, Frank T.; Newman, Morris; Zuckerman, Susan L.
core +1 more source
Inequalities for Binomial Coefficients
Journal of Mathematical Analysis and Applications, 1999 For any real number \(r\) with \(r>1\), let \(c_r= (2\pi(1-{1\over r}))^{-1/2}\) and \(d_r= (r-1)/(1-{1\over r})^r\). Let \(B_{2m}\) \((m= 1,2,\dots)\) be the Bernoulli numbers defined by \[ {z\over e^z-1}=1-{z\over 2}+\sum^\infty_{m=1} B_{2m}{z^{2m}\over (2m)!}.
openaire +2 more sources
Plane Partitions and a Problem of Josephus
Mathematics, 2023 The Josephus Problem is a mathematical counting-out problem with a grim description: given a group of n persons arranged in a circle under the edict that every kth person will be executed going around the circle until only one remains, find the position ...
Mircea Merca
doaj +1 more source
A generalization of the binomial coefficients
Discrete Mathematics, 1992 We pose the question of what is the best generalization of the factorial and the binomial coefficient. We give several examples, derive their combinatorial properties, and demonstrate their interrelationships. On cherche ici à déterminer est la meilleure généralisation possible des factorielles et des coefficients du binôome. On s'interesse à plusieurs
openaire +3 more sources