Add to ORKGExponentiating the hypergeometric series 0FL(1,1,...,1;z), L = 0,1,2,..., furnishes a recursion relation for the members of certain integer sequences bL(n), n = 0,1,2,.... For L >= 0, the bL(n)'s are generalizations of the conventional Bell numbers, b0(n). The corresponding associated Stirling numbers of the second kind are also investigated. For L = 1 one can give a combinatorial interpretation of the numbers b1(n) and of some Stirling numbers associated with them. We also consider the L>1 analogues of Bell numbers for restricted partitions
AbstractLetting Bn(x) the n-th Bell polynomial, it is well known that Bn admit specific integer coor...
In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (an...
We review the history and various approaches to the derivation of Stirling’s series. We use a differ...
and other research outputs Extended Bell and Stirling numbers from hypergeomet-ric exponentiatio
AbstractWe define the potential polynomial F(z)k and the exponential Bell polynomial Bn,j (0,...,0, ...
AbstractThe domains of the Stirling numbers of both kinds are extended from N2 to Z2. These extensio...
AbstractSome years ago Gessel [8] gave a q-analogue of the celebrated exponential formula. We presen...
Let B. denote the number ofpartitions ofa set of n distinct objects. B. are sometimes called exponen...
The aim of this paper is to answer an open problem posed by M. B. Villarino [arXiv:0707.3950v2]. We ...
AbstractIn this paper, we propose another yet generalization of Stirling numbers of the first kind f...
AbstractThe value of the (exponential) complete Bell polynomials for certain arguments, given essent...
Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can b...
We present new proofs for some summation identities involving Stirling numbers of both first and sec...
AbstractSix different formulations equivalent to the statement that, for n ⩾ 2, the sum ∑k = 1n (−1)...
This article introduces a remarkable class of combinatorial numbers, the Stirling set numbers. They...
AbstractLetting Bn(x) the n-th Bell polynomial, it is well known that Bn admit specific integer coor...
In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (an...
We review the history and various approaches to the derivation of Stirling’s series. We use a differ...
and other research outputs Extended Bell and Stirling numbers from hypergeomet-ric exponentiatio
AbstractWe define the potential polynomial F(z)k and the exponential Bell polynomial Bn,j (0,...,0, ...
AbstractThe domains of the Stirling numbers of both kinds are extended from N2 to Z2. These extensio...
AbstractSome years ago Gessel [8] gave a q-analogue of the celebrated exponential formula. We presen...
Let B. denote the number ofpartitions ofa set of n distinct objects. B. are sometimes called exponen...
The aim of this paper is to answer an open problem posed by M. B. Villarino [arXiv:0707.3950v2]. We ...
AbstractIn this paper, we propose another yet generalization of Stirling numbers of the first kind f...
AbstractThe value of the (exponential) complete Bell polynomials for certain arguments, given essent...
Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can b...
We present new proofs for some summation identities involving Stirling numbers of both first and sec...
AbstractSix different formulations equivalent to the statement that, for n ⩾ 2, the sum ∑k = 1n (−1)...
This article introduces a remarkable class of combinatorial numbers, the Stirling set numbers. They...
AbstractLetting Bn(x) the n-th Bell polynomial, it is well known that Bn admit specific integer coor...
In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (an...
We review the history and various approaches to the derivation of Stirling’s series. We use a differ...