Results 71 to 80 of about 100,582 (149)

On congruences related to central binomial coefficients, harmonic and Lucasnumbers

TURKISH JOURNAL OF MATHEMATICS, 2016
Summary: In this paper, using some combinatorial identities, we present new congruences involving central binomial coefficients and harmonic, Catalan, and Fibonacci numbers. For example, for an odd prime \(p\), we have \[\begin{aligned} \sum\limits_{k=1}^{\left( p-1\right) /2}\left( -1\right) ^{k}\binom{2k}{k} H_{k-1} &\equiv \frac{2^{p}}{p}\left( 2F_ ...
KOPARAL, SİBEL, ÖMÜR, NEŞE
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An identity for the central binomial coefficient

, 2012
We find the joint distribution of three simple statistics on lattice paths of n upsteps and n downsteps leading to a triple sum identity for the central binomial coefficient {2n}-choose-{n}. We explain why one of the constituent double sums counts the irreducible pairs of compositions considered by Bender et al., and we evaluate some of the other sums.
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The Series of Reciprocals of Non-central Binomial Coefficients

American Journal of Computational Mathematics, 2013
Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients.
Laiping Zhang, Wanhui Ji
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Central binomial coefficients also count (2431,4231,1432,4132)-avoiders

, 2015
This short paper is concerned with the enumeration of permutations avoiding the following four patterns: $2431$, $4231$, $1432$ and $4132$. Using a bijective construction, we prove that these permutations are counted by the central binomial coefficients.
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Agglomeration Economies and Location Choices by Foreign Firms in Vietnam [PDF]

This paper studies the effects of agglomeration economies on the location choices by foreign firms in Vietnam. By using a large dataset that provides detailed information about individual firms, the study examines the location choices by 568 newly ...
Dinh Thi Thanh Binh
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SUMS OF SERIES INVOLVING CENTRAL BINOMIAL COEFFICIENTS & HARMONIC NUMBERS

, 2018
This paper contains a number of series whose coefficients are products of central binomial coefficients & harmonic numbers. An elegant sum involving $ (2)$ and two other nice sums appear in the last section.
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Congruences involving the reciprocals of central binomial coefficients

, 2009
We present several congruences modulo a power of prime $p$ concerning sums of the following type $\sum_{k=1}^{p-1}{m^k\over k^r}{2k\choose k}^{-1}$ which reveal some interesting connections with the analogous infinite series.
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Fifteen series on harmonic numbers and quintic central binomial coefficients [PDF]

Discrete Mathematics Letters
Chunli Li, Wenchang Chu
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Further Classes of Series Involving Central Binomial Coefficients

Departing from a class of infinite series with central binomial coefficients in the numerator and depending on a positive integer parameter, we first extend known identities to all complex parameters. Then we use various methods, including exponential Bell polynomials and integral representations, to further extend these results.
Dilcher, Karl, Vignat, Christophe
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Asymptotic Expansions of Central Binomial Coefficients and Catalan Numbers

Journal of integer sequences, 2013
We give a systematic view of the asymptotic expansion of two well-known sequences, the central binomial coefficients and the Catalan numbers. The main point is explanation of the nature of the best shift in variable $n$, in order to obtain ``nice'' asymptotic expansions. We also give a complete asymptotic expansion of partial sums of these sequences.
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