Results 41 to 50 of about 97,613 (280)
, 2014 We discuss divisibility properties of some differences of the central binomial coefficients and Catalan numbers. The main tool is the application of various congruences modulo high prime powers for binomial coefficients combined with some recurrences relevant to these combinatorial quantities.
Tamás Lengyel
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On an upper bound for central binomial coefficients and Catalan numbers [PDF]
Recently, Agievich proposed an interesting upper bound on binomial coefficients in the de Moivre-Laplace form. In this article, we show that the latter bound, in the specific case of a central binomial coefficient, is larger than the one proposed by Sasvari and obtained using the Binet formula for the Gamma function.
Jean‐Christophe Pain
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Asymptotics of partial sums of central binomial coefficients and Catalan numbers
, 2009 We prove exact asymptotic expansions for the partial sums of the sequences of central binomial coefficients and Catalan numbers, $\sum_{k=0}^n \binom{2k}{k}$ and $\sum_{k=0}^n C_n$. We also obtain closed forms for the polynomials $\sum_{k=0}^{q-1}\binom{2k}{k}x^k$ and $\sum_{k=0}^{q-1}C_kx^k$ over the field of $p$ elements, where $q$ is a power of the ...
Sandro Mattarei
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Binomial Sum Relations Involving Fibonacci and Lucas Numbers
AppliedMath, 2023 In this paper, we provide a first systematic treatment of binomial sum relations involving (generalized) Fibonacci and Lucas numbers. The paper introduces various classes of relations involving (generalized) Fibonacci and Lucas numbers and different ...
Kunle Adegoke +2 more
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Infinite series about harmonic numbers inspired by Ramanujan–like formulae
Electronic Research Archive, 2023 By employing the coefficient extraction method from hypergeometric series, we shall establish numerous closed form evaluations for infinite series containing central binomial coefficients and harmonic numbers, including several conjectured ones made by Z.
Chunli Li, Wenchang Chu
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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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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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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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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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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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