The Method of Coefficients

Merlini, Donatella; Sprugnoli, Renzo; Verri, M. Cecilia

doi:10.1080/00029890.2007.11920390

Cited by 52 publications

(36 citation statements)

References 11 publications

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“…[t n ] are called the ''coefficient of '' functionals [8]. If f (t) and g(t) are formal power series, the following relations hold [8]:…”

Section: Introductionmentioning

confidence: 99%

Sums of products of Cauchy numbers

Zhao

2009

Discrete Mathematics

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a b s t r a c tIn this paper, we consider a kind of sums involving Cauchy numbers, which have not been studied in the literature. By means of the method of coefficients, we give some properties of the sums. We further derive some recurrence relations and establish a series of identities involving the sums, Stirling numbers, generalized Bernoulli numbers, generalized Euler numbers, Lah numbers, and harmonic numbers. In particular, we generalize some relations between two kinds of Cauchy numbers and some identities for Cauchy numbers and Stirling numbers.

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“…[t n ] are called the ''coefficient of '' functionals [8]. If f (t) and g(t) are formal power series, the following relations hold [8]:…”

Section: Introductionmentioning

confidence: 99%

Sums of products of Cauchy numbers

Zhao

2009

Discrete Mathematics

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“…Since g(x) = f ′ (x), from (2) and (5), we have Rs(x) = r(x) and s n = r n−1 (for n 1). So, identity (8) follows immediately from (6).…”

Section: The Main Identitymentioning

confidence: 87%

“…See, for instance, [8]. Moreover, the field of complex numbers will be denoted by C. In what follows, for simplicity, the symbols α, β and q are considered as complex parameters, but more generally they can be considered as indeterminates.…”

Section: Combinatorial Sequencesmentioning

confidence: 99%

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Riordan matrices and sums of harmonic numbers

Munarini

2011

Appl Anal Discrete Math

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“…The standard work on these techniques is the book of Wilf [18]. These methods are called also as the method of coefficients, see Merlini et al [11] for the compactly review of generating functions tools, connections between g.f., Riordan arrays and inversion formulas.…”

Section: List Of Generating Functionsmentioning

confidence: 99%

Counting Lattice Paths With Four Types of Steps

Dziemiańczuk

2013

Graphs and Combinatorics

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The main purpose of this paper is to derive generating functions for the numbers of lattice paths running from (0, 0) to any (n, k) in Z × N consisting of four types of steps: horizontal, and sloping L = (−1, 1). These paths generalize the well-known Delannoy paths which consist of steps H, V , and D. Several restrictions are considered. However, we mainly treat with those which will be needed to get the generating function for the numbers R(n, k) of these lattice paths whose points lie in the integer rectangle {(x, y) ∈ N 2 : 0 ≤ x ≤ n, 0 ≤ y ≤ k}. Recurrence relation, generating functions and explicit formulas are given. We show that most of considered numbers define Riordan arrays.

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The Method of Coefficients

Cited by 52 publications

References 11 publications

Sums of products of Cauchy numbers

Sums of products of Cauchy numbers

Riordan matrices and sums of harmonic numbers

Counting Lattice Paths With Four Types of Steps

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