On the central antecedents of integer (And other) sequences

Paul Barry

On the central antecedents of integer (And other) sequences

Paul Barry

School of Science and Computing

Research output: Contribution to journal › Article › peer-review

Abstract

With each power series g(x) with g(0) ≠ 0, we associate a power series G(x) such that [xⁿ]G(x)ⁿ = [xⁿ]g(x). We give examples for well-known integer sequences, including the Catalan numbers and generalized Catalan numbers, and explore the antecedents of rational sequences, including the Bernoulli numbers and the harmonic numbers.

Original language	English
Article number	20.8.3
Pages (from-to)	1-7
Number of pages	7
Journal	Journal of Integer Sequences
Volume	23
Issue number	8
Publication status	Published - 2020

Keywords

Bernoulli number
Catalan number
Central coefficient
Generating function
Harmonic number
Lagrange inversion
Lambert function
Partition number

Cite this

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abstract = "With each power series g(x) with g(0) ≠ 0, we associate a power series G(x) such that [xn]G(x)n = [xn]g(x). We give examples for well-known integer sequences, including the Catalan numbers and generalized Catalan numbers, and explore the antecedents of rational sequences, including the Bernoulli numbers and the harmonic numbers.",

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KW - Central coefficient

KW - Generating function

KW - Harmonic number

KW - Lagrange inversion

KW - Lambert function

KW - Partition number

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On the central antecedents of integer (And other) sequences

Abstract

Keywords

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