A Combinatorial Interpretation for Sequence A345973 in OEIS

TL;DR

This paper provides a combinatorial interpretation of OEIS sequence A345973 using bicolored ordered trees, linking its generating function to a specific product and sum identity.

Contribution

It introduces a novel combinatorial model for the sequence, connecting it to bicolored ordered trees and a unique generating function identity.

Findings

Sequence A345973 characterized by a new combinatorial interpretation.

Generating function linked to bicolored ordered trees and a product identity.

Provides insight into the structure of the sequence through combinatorial means.

Abstract

We give a combinatorial interpretation in terms of bicolored ordered trees for the sequence (a_n)_{n>=1}=(1, 1, 1, 2, 3, 6, 10, 20, 36, 73,... ), A345973 in OEIS, whose generating function satisfies the defining identity Sum_{n>=1}a_n x^n = x + x^2/Product_{n>=1}(1 - a_n x^n).