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Natalini, Pierpaolo; Ricci, Paolo Emilio

Integer sequences connected with extensions of the Bell polynomials. (English) Zbl 1387.11019

J. Integer Seq. 20, No. 10, Article 17.10.2, 13 p. (2017).
Summary: The Encyclopedia of Integer Sequences [http://oeis.org/] includes some sequences that are connected with the Bell numbers and that have a particular combinatorial meaning. In this article, we find a general meaning for framing sequences, including the above mentioned ones. Furthermore, by using Laguerre-type derivatives, we derive the Laguerre-type Bell numbers of higher order, showing, as a by-product, that it is possible to construct new integer sequences which are not included in the Encyclopedia.

Cited in 1 Document

MSC:

11B73 Bell and Stirling numbers
05A17 Combinatorial aspects of partitions of integers
11P81 Elementary theory of partitions

Keywords:

higher order Bell polynomial; higher order Bell number; combinatorial analysis; partition; Laguerre-type Bell numbers of higher order; OEIS

Software:

OEIS
Cite Review PDF
Full Text: Link

Online Encyclopedia of Integer Sequences:

Number of n-step mappings with 4 inputs.
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where the e.g.f. of column k is 1+g^(k+1)(x) with g = x-> exp(x)-1.

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