Preprint Article Version 1 This version is not peer-reviewed

# Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius–Euler Numbers

Version 1 : Received: 4 August 2017 / Approved: 4 August 2017 / Online: 4 August 2017 (15:47:44 CEST)

How to cite: Qi, F.; Niu, D.; Guo, B. Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius–Euler Numbers. Preprints 2017, 2017080017 (doi: 10.20944/preprints201708.0017.v1). Qi, F.; Niu, D.; Guo, B. Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius&ndash;Euler Numbers. Preprints 2017, 2017080017 (doi: 10.20944/preprints201708.0017.v1).

## Abstract

In the paper, by virtue of the Faa di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.

## Subject Areas

simplification; coefficient; ordinary differential equation; higher order Frobenius–Euler number; Faa di Bruno formula; Bell polynomial of the second kind; inversion formula