Results 31 to 40 of about 165,496 (329)
Some combinatorial identities containing central binomial coefficients or Catalan numbers*
Applied Mathematics in Science and Engineering, 2023 In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four ...
Feng Qi, Da-Wei Niu, Dongkyu Lim
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On Binomial Coefficient Residues [PDF]
Canadian Journal of Mathematics, 1957 The number of binomial coefficients , which are congruent to j , 0 ≤ j ≤ p − 1, modulo the prime number p is denoted by θj(n). In this paper we give systems of simultaneous linear difference equations with constant coefficients whose
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Reduction of the sum of the weight equal powers to explicit combinatorial representation
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012 The paper contains the proof of the statement that the component of the sum of weighted powers with natural bases and equal parameters, dependent on weight coefficients, is equal to the sum of products of binomial and weight coefficients.
A. I. Nikonov
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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
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Some congruences involving binomial coefficients
, 2015 Binomial coefficients and central trinomial coefficients play important roles in combinatorics. Let $p>3$ be a prime. We show that $$T_{p-1}\equiv\left(\frac p3\right)3^{p-1}\ \pmod{p^2},$$ where the central trinomial coefficient $T_n$ is the constant ...
Cao, Hui-Qin, Sun, Zhi-Wei
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Binomial Series without Binomial Coefficients
, 2023 Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical equations for solving today’s scientific problems and challenges. Also, the computational science is a rapidly growing interdisciplinary area where science, computation, mathematics, and its collaboration use advanced computing ...
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A new generalization of binomial coefficients
, 2013 Let $t$ be a fixed parameter and $x$ some indeterminate. We give some properties of the generalized binomial coefficients $\genfrac{}{0pt}{}{x}{k}$ inductively defined by $k/x \genfrac{}{0pt}{}{x}{k}= t\genfrac{}{0pt}{}{x-1}{k-1} +(1-t)\genfrac{}{0pt ...
Lassalle, Michel
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Molecular Oncology, EarlyView.A‐to‐I editing of miRNAs, particularly miR‐200b‐3p, contributes to HGSOC progression by enhancing cancer cell proliferation, migration and 3D growth. The edited form is linked to poorer patient survival and the identification of novel molecular targets.
Magdalena Niemira +14 more
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The update exposition of the components organising the sum of weighted equal powers
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012 The sum of the weighted equal powers with natural bases and parameters is organized of components, which are independent or dependent on weight coefficients.
A. I. Nikonov
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An overpartition analogue of the $q$-binomial coefficients [PDF]
, 2014 We define an overpartition analogue of Gaussian polynomials (also known as $q$-binomial coefficients) as a generating function for the number of overpartitions fitting inside the $M \times N$ rectangle.
Dousse, Jehanne, Kim, Byungchan
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