Some identities on r-central factorial numbers and r-central Bell polynomials

Some combinatorial formulas for the partial r-Bell polynomials

The partial r-Bell polynomials generalize the classical partial Bell polynomials (coinciding with them when r = 0) by assigning a possibly different set of weights to the blocks containing the r smallest elements of a partition no two of which are allowed to belong to the same block. In this paper, we study the partial r-Bell polynomials from a combinatorial standpoint and derive several new fo...

Linear Recurrences for r-Bell Polynomials

Letting Bn,r be the n-th r-Bell polynomial, it is well known that Bn(x) admits specific integer coordinates in the two bases {x}i and {xBi(x)}i according to, respectively, the Stirling numbers and the binomial coefficients. Our aim is to prove that the sequences Bn+m,r(x) and Bn,r+s(x) admit a binomial recurrence coefficient in different bases of the Q-vector space formed by polynomials of Q[X].

r-Bell polynomials in combinatorial Hopf algebras

We introduce partial r-Bell polynomials in three combinatorial Hopf algebras. We prove a factorization formula for the generating functions which is a consequence of the Zassenhauss formula. Résumé Les r−polynômes de Bell dans des algèbres de Hopf combinatoires Nous définissons des polynômes r-Bell partiels dans trois algèbres de Hopf combinatoires. Nous prouvons une formule de factorisation po...

Identities on Bell polynomials and Sheffer sequences

In this paper, we study exponential partial Bell polynomials and Sheffer sequences. Two new characterizations of Sheffer sequences are presented, which indicate the relations between Sheffer sequences and Riordan arrays. Several general identities involving Bell polynomials and Sheffer sequences are established, which reduce to some elegant identities for associated sequences and cross sequences.

Bell polynomials and Fibonacci numbers