On the Central Antecedents of Integer (and Other) Sequences
Paul Barry
School of Science
Waterford Institute of Technology
Ireland
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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(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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