The generating function of A348410 in OEIS using the diagonal method

TL;DR

This paper derives an algebraic equation for the generating function of sequence A348410 using the diagonal method, Hautus and Klarner's approach, and the Gfun software.

Contribution

It applies a classical diagonal method combined with modern computational tools to explicitly find the generating function for a specific OEIS sequence.

Findings

Derived an algebraic equation for the generating function g(z).

Connected historical methods with modern computational tools.

Provided explicit form for the generating function of A348410.

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 $g(z)=\sum_na_nz^n$.