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We derive a closed form for the generalized Bernoulli polynomial of order $n$ in terms of Bell polynomials and Stirling numbers of the second kind using the Fa\`a di Bruno's formula.

In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.

In this paper, by virtue of a determinantal formula for derivatives of the ratio between two differentiable functions, in view of the Fa\`a di Bruno formula, and with the help of several identities and closed-form formulas for the partial…

In this paper, we consider the poly-Bernoulli numbers and polynomials of the second kind and presents new and explicit formulae for calculating the poly-Bernoulli numbers of the second kind and the Stirling numbers of the second kind.

In the paper, by virtue of the famous formula of Fa\`a di Bruno, with the aid of several identities of partial Bell polynomials, by means of a formula for derivatives of the ratio of two differentiable functions, and with availability of…

In this brief note, we give two explicit formulas for the Bernoulli Numbers in terms of the Stirling numbers of the second kind, and the Eulerian Numbers. To the best of our knowledge, these formulas are new. We also derive two more…

In the paper, the author finds an explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind.

In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.

In the paper, the authors establish an explicit formula for computing Bernoulli polynomials at non-negative integer points in terms of $r$-Stirling numbers of the second kind.

In the note, the author discovers an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.

In the paper, the authors review some explicit formulas and establish a new explicit formula for Bernoulli and Genocchi numbers in terms of Stirling numbers of the second kind.

In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the…

In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.

In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also…

This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.

In the paper, with the aid of the Fa\`a di Bruno formula, in terms of central factorial numbers of the second kind, and with the terminology of the Stirling numbers of the second kind, the authors derive several series expansions for any…

We review and discuss some results on the representation of Bernoulli, poly-Bernoulli numbers, and Bernoulli and Cauchy polynomials in terms of Stirling numbers of the first or second kind, or in terms of r-Stirling numbers.

In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…

In this paper, by introducing the degenerate Fubini-type polynomials, we give several relations with the help of the Fa\`a di Bruno formula and some properties of Bell polynomials, and generating function methods. Also, we derive some new…

The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.