Submitted:
10 August 2017
Posted:
11 August 2017
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Abstract
In the paper, using two inversion theorems for the Stirling numbers and binomial coecients, employing properties of the Bell polynomials of the second kind, and utilizing a higher order derivative formula for the ratio of two di erentiable functions, the authors present two explicit formulas, a determinantal expression, and a recursive relation for a sequence of unnamed polynomials, derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, and recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials.
Keywords:
identity
; Bell polynomial
; unnamed polynomial
; explicit formula
; inversion theorem
; Stirling number
; binomial coefficient
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