## Abstract

We initiate the study of the coefficients of the distinct monomials in the expansion of the multivariate polynomials x_{1}(x_{1} +x_{2})···(x_{1} +x_{2} +···+x_{n}),n ∈ ℕ, the number of which was shown by Shallit to be counted by the Catalan numbers C_{n},n ∈ ℕ. In particular, we obtain an exact formula for the coefficients and reduce the complexity of the search for their maximum from the order of C_{n} to the order of the number of partitions of n with distinct parts.

Original language | English |
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Article number | 22.4.2 |

Journal | Journal of Integer Sequences |

Volume | 25 |

Issue number | 4 |

State | Published - 1 Jan 2022 |

## Keywords

- Catalan number
- combinatorial optimization problem
- integer partition
- multivariate polynomial

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

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