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

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 $g(z)={\sum }_n{a}_n{z}^n$. The second identity uses the \emph{generalized binomial series}, popularized in the textbook \emph{Concrete mathematics}.

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