The generating function of A348410 in OEIS using the diagonal method and another sequence (A001008) from OEIS

Helmut Prodinger

The generating function of A348410 in OEIS using the diagonal method and another sequence (A001008) from OEIS

Combinatorics 2026-05-26 v2

Authors: Helmut Prodinger

Abstract

$a_n=[x^n](1-x)^{-n}(1-x^2)^{-n}$ is the sequence A348410 in the Encyclopedia of Integer Sequences. Using a method from Hautus and Klarner from 1971 and the software \textsf{Gfun} we find an algebraic equation for the generating function $g(z)=\sum_na_nz^n$ . The second identity uses the \emph{generalized binomial series}, popularized in the textbook \emph{Concrete mathematics}.

Cite

@article{arxiv.2605.21255,
  title  = {The generating function of A348410 in OEIS using the diagonal method and another sequence (A001008) from OEIS},
  author = {Helmut Prodinger},
  journal= {arXiv preprint arXiv:2605.21255},
  year   = {2026}
}

Comments

A new sequence (A001008) has been added to the discussion. Title has been changed accordingly

The generating function of A348410 in OEIS using the diagonal method and another sequence (A001008) from OEIS

Abstract

Cite

Comments

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