Journal of Integer Sequences, Vol. 22 (2019), Article 19.3.8

Nonlinear Inverse Relations for Bell Polynomials via the Lagrange Inversion Formula

Jin Wang
Department of Mathematics
Zhejiang Normal University
Jinhua 321004
P. R. China


In this paper, by using the classical Lagrange inversion formula, we establish a nonlinear inverse relation that involves the Bell polynomials. As applications of this inverse relation, we not only find a short proof of another nonlinear inverse relation due to Birmajer et al., but also deduce some allied combinatorial identities. Finally, we propose the general problem of finding nonlinear inverse relations and give a positive solution to it.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A111785 A133932 A134264 A178867 A187082 A263633.)

Received July 9 2018; revised versions received October 17 2018; March 25 2019; March 31 2019. Published in Journal of Integer Sequences, May 22 2019.

Return to Journal of Integer Sequences home page