Results 11 to 20 of about 100,720 (284)

Spatiotemporal Trends and Co-Resistance Patterns of Multidrug-Resistant Enteric <i>Escherichia coli</i> O157 Infections in Humans in the United States. [PDF]

Pathogens
Multidrug-resistant (MDR) Shiga toxin-producing Escherichia coli O157 (STEC O157) is a public health threat. This study analyzed publicly available surveillance data collected by the National Antimicrobial Resistance Monitoring System (NARMS) to assess ...
Bhatt T, Varga C.
europepmc   +2 more sources

Congruences involving the reciprocals of central binomial coefficients [PDF]

, 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.
Roberto Tauraso
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INTEGRAL REPRESENTATIONS AND INEQUALITIES OF EXTENDED CENTRAL BINOMIAL COEFFICIENTS [PDF]

, 2021
In the paper, the author presents three integral representations of extended central binomial coefficient, proves decreasing and increasing properties of two power-exponential functions involving extended (central) binomial coefficients, derives several double inequalities for bounding extended (central) binomial coefficient, and compares with known ...
Chunfu Wei
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Products and Sums Divisible by Central Binomial Coefficients [PDF]

The Electronic Journal of Combinatorics, 2013
In this paper we study products and sums divisible by central binomial coefficients. We show that $$2(2n+1)\binom{2n}n\ \bigg|\ \binom{6n}{3n}\binom{3n}n\ \ \mbox{for all}\ n=1,2,3,\ldots.$$ Also, for any nonnegative integers $k$ and $n$ we have $$\binom {2k}k\ \bigg|\ \binom{4n+2k+2}{2n+k+1}\binom{2n+k+1}{2k}\binom{2n-k+1}n$$ and $$\binom{2k}k\ \bigg|\
Zhi‐Wei Sun
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Sums of series involving central binomial coefficients & harmonic numbers [PDF]

, 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.
Amrik Singh Nimbran
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Central binomial coefficients also count (2431,4231,1432,4132)-avoiders [PDF]

, 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.
Marie-Louise Bruner
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Integral Representations of Catalan Numbers and Sums Involving Central Binomial Coefficients

, 2023
In the paper, the authors collect several integral representations of the Catalan numbers and central binomial coefficients, supply alternative proofs of two integral representations of the Catalan numbers, and apply these integral representations to alternatively prove several combinatorial identities for finite and infinite sums in which central ...
Bai‐Ni Guo, Dongkyu Lim
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ON SOME CONGRUENCES INVOLVING CENTRAL BINOMIAL COEFFICIENTS

Bulletin of the Australian Mathematical Society
AbstractWe prove the following conjecture of Z.-W. Sun [‘On congruences related to central binomial coefficients’, J. Number Theory13(11) (2011), 2219–2238]. Let p be an odd prime. Then $$ \begin{align*} \sum_{k=1}^{p-1}\frac{\binom{2k}k}{k2^k}\equiv-\frac12H_{{(p-1)}/2}+\frac7{16}p^2B_{p-3}\pmod{p^3}, \end{align*} $$ where $H_n$ is the nth harmonic
Guo-Shuai Mao
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On congruences related to central binomial coefficients [PDF]

Journal of Number Theory, 2009
It is known that $\sum_{k=0}^\infty\binom{2k}{k}/((2k+1)4^k)= /2$ and $\sum_{k=0}^\infty\binom{2k}{k}/((2k+1)16^k)= /3$. In this paper we obtain their p-adic analogues such as $$\sum_{p/23 is a prime and E_0,E_1,E_2,... are Euler numbers. Besides these, we also deduce some other congruences related to central binomial coefficients.
Zhi‐Wei Sun
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An identity for the central binomial coefficient [PDF]

, 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.
David Callan
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