Journal of Integer Sequences, Vol. 23 (2020), Article 20.8.3

On the Central Antecedents of Integer (and Other) Sequences

Paul Barry
School of Science
Waterford Institute of Technology


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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(Concerned with sequences A000027 A000041 A000108 A000203 A000984 A002426 A005043 A007317 A025174 A214776.)

Received June 23 2020; revised version received September 2 2020. Published in Journal of Integer Sequences, September 2 2020.

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