In this paper, the author presents several closed forms and determinantal expressions involving Stirling numbers of second kind for higher-order Bernoulli Euler polynomials by applying Faà di Bruno formula some properties Bell polynomials.

In the paper, making use of two inversion theorems for the Stirling numbers and binomial coefficients, the authors present an alternative explicit formula 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. 1. M...

In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations properties including summation formulas related to Bell numbers kind. Then, introduce Bernoulli order α investigate multifarious correlations derivative properties. Also, acquire diverse implicit symmetric identities for α. Moreover, attain several interesting arising from umbral calcu...

In this paper we give a simple algorithm to generate all partitions of {1, 2, · · · , n} into k non-empty subsets. The number of such partitions is known as the Stirling number of the second kind. The algorithm generates each partition in constant time without repetition. By choosing k = 1, 2, · · · , n we can also generate all partitions of {1, 2, · · · , n} into subsets. The number of such pa...