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Applied Mathematics and Computation, ISSN 0096-3003, 09/2013, Volume 220, pp. 482 - 486
In this study, Fibonacci and Lucas numbers have been obtained by using generalized Fibonacci numbers. In addition, some new properties of generalized Fibonacci... 
Lucas number | Generalized Fibonacci number | Binomial coefficients | Fibonacci number | MATHEMATICS, APPLIED
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 04/2019, Volume 69, Issue 2, pp. 327 - 338
Sums of products of two Gaussian -binomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight... 
Primary 11B39 | Secondary 05A30 | binomial coefficients | Fibonomial and Lucanomial coefficients | sums identites | partial fraction decomposition | Gaussian | Gaussian q-binomial coefficients | MATHEMATICS | GENERALIZED FIBONACCI | IDENTITIES | FIBONOMIAL SUMS
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 5/2014, Volume 34, Issue 1, pp. 143 - 156
Let t be a fixed parameter and x some indeterminate. We give some properties of the generalized binomial coefficients $\genfrac{\langle... 
Generalized binomial coefficients | Fourier Analysis | Functions of a Complex Variable | 05A10 | Field Theory and Polynomials | 11B65 | Mathematics | Number Theory | Combinatorics | MATHEMATICS | PROOFS | IDENTITIES
Journal Article
SpringerPlus, ISSN 2193-1801, 12/2014, Volume 3, Issue 1, pp. 1 - 7
The Intraclass Correlation Coefficient (ICC) is commonly used to estimate the similarity between quantitative measures obtained from different sources.... 
Negative binomial mixed model | Intraclass correlation coefficient | Variance components | Generalized linear mixed model | Science, general | MODELS | MULTIDISCIPLINARY SCIENCES
Journal Article
Discrete Mathematics, ISSN 0012-365X, 08/2012, Volume 312, Issue 15, pp. 2197 - 2202
We obtain explicit formulas that express the complete homogeneous symmetric polynomials of the sequence of partial sums sk of a sequence xk as polynomials in... 
Legendre–Stirling numbers | Symmetric polynomials | Gaussian coefficients | Generalized Stirling numbers | [formula omitted]-Stirling numbers | q-Stirling numbers | Legendre-Stirling numbers | MATHEMATICS | DIVIDED DIFFERENCES | PASCAL MATRICES
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 01/2014, Volume 21, Issue 1
We work with a generalization of Stirling numbers of the second kind related to the boson normal ordering problem (P. Blasiak et al.). We show that these... 
Powers of binomial coefficients | Generalized stirling numbers | MATHEMATICS | MATHEMATICS, APPLIED | generalized Stirling numbers | powers of binomial coefficients
Journal Article
Journal of Number Theory, ISSN 0022-314X, 10/2014, Volume 143, pp. 293 - 319
For any positive integer n and variables a and x we define the generalized Legendre polynomial Pn(a,x) by Pn(a,x)=∑k=0n(ak)(−1−ak)(1−x2)k. Let p be an odd... 
Generalized Legendre polynomial | Binomial coefficient | Congruence | MATHEMATICS | PRODUCTS | BINOMIAL COEFFICIENTS | SUMS
Journal Article
Integers, ISSN 1867-0652, 06/2009, Volume 9, Issue 2, pp. 167 - 175
The Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete... 
partial autocorrelations | Binomial coefficients | Levinson–Durbin–Whittle sequence | Levinson–Durbin sequence | stationary process | generalized Levinson–Durbin sequence
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 2010, Volume 45, Issue 4, pp. 564 - 606
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 02/2019, Volume 758, pp. 42 - 60
We pursue the investigation of generalizations of the Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of... 
Binomial coefficients of words | Bertrand numeration systems | Generalized Pascal triangles | Parry numbers | Perron numbers | β-expansions | COEFFICIENTS | COMPUTER SCIENCE, THEORY & METHODS | beta-expansions
Journal Article
Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 06/2018, Volume 67, pp. 71 - 77
In this paper we present theoretical and computational results regarding generalized arithmetic m-triangles. The numerical values recover well-known number... 
asympotic formulae | pentanomial numbers | generalized binomial coefficients | recurrent sequences
Journal Article
Journal of Lie Theory, ISSN 0949-5932, 2016, Volume 26, Issue 2, pp. 439 - 477
We introduce some multivariate analogues of Meixner, Charlier and Krawtchouk polynomials, and establish their main properties by using analysis on symmetric... 
Symmetric cones | Spherical polynomials | Generalized binomial coeffcients | Multivariate analysis | Discrete orthogonal polynomials | MATHEMATICS | spherical polynomials | symmetric cones | generalized binomial coefficients | discrete orthogonal polynomials
Journal Article
Biometrika, ISSN 0006-3444, 9/2009, Volume 96, Issue 3, pp. 735 - 749
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2017, Volume 86, Issue 304, pp. 899 - 933
We define a Gauss factorial N_n! to be the product of all positive integers up to N that are relatively prime to n\in \mathbb{N}. In this paper we study... 
Generalized Fermat numbers | Congruences | Gauss-Wilson theorem | Gauss factorials | Binomial coefficient congruences | Factors | MATHEMATICS, APPLIED | generalized Fermat numbers | congruences | GAUSS | MULTIPLICATIVE ORDERS | binomial coefficient congruences | factors
Journal Article
Fisheries Research, ISSN 0165-7836, 2007, Volume 84, Issue 2, pp. 210 - 221
The zero-inflated negative binomial (ZINB) regression model with smoothing is introduced for modeling count data with many zero-valued observations, and its... 
Spline smoothing | CPUE | GAM | Zero-inflated | Shark | Negative binomial | GLM | EM algorithm | shark | STANDARDIZATION | spline smoothing | PELAGIC SHARKS | GENERALIZED LINEAR-MODELS | FISHERY | CATCH RATES | FISHERIES | ABUNDANCE DATA | negative binomial | POISSON REGRESSION | zero-inflated | SELECTION | LIKELIHOOD | INDEXES | Analysis | Models | Algorithms
Journal Article
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