# The hafnian of Toeplitz matrices of a special type, perfect matchings and Bessel polynomials

## TL;DR

This paper introduces a straightforward formula for efficiently computing the hafnian of a specific class of Toeplitz matrices, linking the results to perfect matchings and Bessel polynomials.

## Contribution

It provides a novel analytical formula for the hafnian of certain Toeplitz matrices, enhancing computational efficiency and theoretical understanding.

## Key findings

- Derived a simple formula for the hafnian of special Toeplitz matrices
- Connected hafnian computation to perfect matchings and Bessel polynomials
- Facilitated exact and efficient calculations for these matrices

## Abstract

We present a simple and convenient analytical formula for efficient exact computation of the hafnian of Toeplitz matrices of a special type. An interpretation of the obtained results is given in the language of perfect matchings and Bessel polynomials.