Results 11 to 20 of about 25,001 (275)
Central binomial coefficients divisible by or coprime to their indices [PDF]
International Journal of Number Theory, 2017 Let A be the set of all positive integers n such that n divides the central binomial coefficient (2nn). Pomerance proved that the upper density of A is at most 1−log2. We improve this bound to 1−log2−0.05551.
Sanna, Carlo, Carlo Sanna
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On a divisor of the central binomial coefficient [PDF]
The Ramanujan Journal, 2021 It is well known that for all $n\geq1$ the number $n+ 1$ is a divisor of the central binomial coefficient ${2n\choose n}$. Since the $n$th central binomial coefficient equals the number of lattice paths from $(0,0)$ to $(n,n)$ by unit steps north or east, a natural question is whether there is a way to partition these paths into sets of $n+ 1$ paths or
Matthew Just, Maxwell Schneider
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Series of Convergence Rate −1/4 Containing Harmonic Numbers
Axioms, 2023 Two general transformations for hypergeometric series are examined by means of the coefficient extraction method. Several interesting closed formulae are shown for infinite series containing harmonic numbers and binomial/multinomial coefficients.
Chunli Li, Wenchang Chu
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Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers
Mathematics, 2022 Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo, Wenchang Chu
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A note on a one-parameter family of non-symmetric number triangles [PDF]
Opuscula Mathematica, 2012 The recent growing interest in special Clifford algebra valued polynomial solutions of generalized Cauchy-Riemann systems in \((n + 1)\)-dimensional Euclidean spaces suggested a detailed study of the arithmetical properties of their coefficients, due to ...
Maria Irene Falcão, Helmuth R. Malonek
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Some Families of Apéry-Like Fibonacci and Lucas Series
Mathematics, 2021 In this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also pointed ...
Robert Frontczak +2 more
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The Design of the Internal Audit implementation Model in the Iranian Public Sector Institutions [PDF]
مطالعات تجربی حسابداری مالی, 2023 Public Sector Internal Audit, by delivering reliable and consulting services in line with improvement and eliminate challenges can support organizations to achieve goals and provide better services. The purpose of this study is to provide a model for the
Jafar Babajani +2 more
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Results in Nonlinear Analysis, 2021 In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing the ratio of two central binomial coefficients which are related to the ...
Feng Qi, Chao-Ping Chen , Dongkyu Lim
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