On the central antecedents of integer (And other) sequences

Paul Barry

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number20.8.3
Pages (from-to)1-7
Number of pages7
JournalJournal of Integer Sequences
Issue number8
Publication statusPublished - 2020


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


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