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A sum of binomial coefficients [PDF]
Mathematics of Computation, 1978 An explicit expression is derived for the sum of the ( k + 1 ) (k + 1) st binomial coefficients in the nth, ( n − m ) (n - m) th, ( n − 2 m ) (n - 2m) th,... row of the arithmetic triangle.
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Binomial-coefficient multiples of irrationals [PDF]
Monatshefte f�r Mathematik, 1998 Denote by $x$ a random infinite path in the graph of Pascal's triangle (left and right turns are selected independently with fixed probabilities) and by $d_n(x)$ the binomial coefficient at the $n$'th level along the path $x$. Then for a dense $G_ $ set of $ $ in the unit interval, $\{d_n(x) \}$ is almost surely dense but not uniformly distributed ...
Petersen, Karl E., Adams, T.M.
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Evaluation of a Special Hankel Determinant of Binomial Coefficients [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 This paper makes use of the recently introduced technique of $\gamma$-operators to evaluate the Hankel determinant with binomial coefficient entries $a_k = (3 k)! / (2k)! k!$. We actually evaluate the determinant of a class of polynomials $a_k(x)$ having
Ömer Eugeciouglu +2 more
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Some properties of binomial coefficients and their application to growth modelling
Arab Journal of Basic and Applied Sciences, 2018 Some properties of diagonal binomial coefficients were studied in respect to frequency of their units’ digits. An approach was formulated that led to the use of difference tables to predict if certain units’ digits can appear in the values of binomial ...
Vladimir L. Gavrikov
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Euler-type sums involving multiple harmonic sums and binomial coefficients
Open Mathematics, 2021 In this paper, we mainly show that generalized Euler-type sums of multiple harmonic sums with reciprocal binomial coefficients can be expressed in terms of rational linear combinations of products of classical multiple zeta values (MZVs) and multiple ...
Si Xin
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Poset binomials and rainbow characters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 This paper introduces a variation on the binomial coefficient that depends on a poset and interpolates between $q$-binomials and 1-binomials: a total order gives the usual $q$-binomial, and a poset with no relations gives the usual binomial coefficient ...
Daniel Bragg, Nathaniel Thiem
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Fractional Sums and Differences with Binomial Coefficients
Discrete Dynamics in Nature and Society, 2013 In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives.
Thabet Abdeljawad +3 more
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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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Sums of Reciprocals of Triple Binomial Coefficients
International Journal of Mathematics and Mathematical Sciences, 2008 We investigate the integral representation of infinite sums involving the reciprocals of triple binomial coefficients. We also recover some wellknown properties of 𝜁(3) and extend the range of results given by other authors.
A. Sofo
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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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