Recurrences of Stirling and Lah numbers via second kind Bell polynomial
Discrete Mathematics Letters, 2020 Summary: In the paper, by virtue of several explicit formulas for special values and a recurrence of the Bell polynomials of the second kind, the authors derive several recurrences for the Stirling numbers of the first and second kinds, for 1-associate Stirling numbers of the second kind, for the Lah numbers, and for the binomial coefficients.
Qi F., Natalini P., Ricci P. E.
openaire +3 more sources
On Stirling and bell numbers of order 1/2
FilomatThe Stirling numbers of order 1/2 (of the second kind) introduced by Katugampola are discussed and it is shown that they are given by a scaled subfamily of the generalized Stirling numbers introduced by Hsu and Shiue. This allows to deduce in a straightforward fashion many properties of the Stirling and Bell numbers of order 1/2, for ...
openaire +1 more source
Extended degenerate Stirling numbers of the second kind and extended degenerate Bell polynomials
, 2017 In a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials associated with them.
Kim, Taekyun, Kim, Dae San
openaire +2 more sources
, 2020 Bell and Stirling numbers of first and second kind tell the number of ways that n objects, or n cycles in the case of Stirling numbers of first kind, can be distributed in k cells. They are usually obtained through recurrence rules. However, recurrence rules only tell how many distributions are possible, not the specific form of each distribution, so ...
openaire +2 more sources
q-Stirling sequence spaces associated with q-Bell numbers
Open MathematicsIn this study, we build qq-analog of the qq-Stirling matrix involved qq-Bell numbers Sq=(Snk(q)){{\mathbb{S}}}_{q}=({S}_{nk}\left(q)) defined by Sq=(Snk(q))=Sq(n,k)Bq(n),0≤k≤n,0,otherwise.\begin{array}{r}{{\mathbb{S}}}_{q}=({S}_{nk}\left(q))=\left ...
Atabey Koray Ibrahim +3 more
doaj +1 more source
An explicit formula for computing Bell numbers in terms of Lah and Stirling numbers
, 2014 3 ...
openaire +2 more sources
Zeros distribution and interlacing property for certain polynomial sequences
Open MathematicsIn this article, we first prove that the Hankel determinant of order three of the polynomial sequence {Pn(x)=∑k≥0P(n,k)xk}n≥0{\left\{{P}_{n}\left(x)={\sum }_{k\ge 0}P\left(n,k){x}^{k}\right\}}_{n\ge 0} is weakly (Hurwitz) stable, where P(n,k)P\left(n,k ...
Guo Wan-Ming
doaj +1 more source
A congeneric and non-randomly associated pair of larval trematodes dominates the assemblage of co-infecting parasites in fathead minnows (<i>Pimephales promelas</i>). [PDF]
Parasitology, 2023 Hirtle SV, Ahn S, Goater CP.
europepmc +1 more source
Making community pharmacies psychologically informed environments (PIE): a feasibility study to improve engagement with people using drug services in Scotland. [PDF]
Prim Health Care Res Dev, 2023 Matheson C +6 more
europepmc +1 more source
SHIFTING POWERS IN SPIVEY'S BELL NUMBER FORMULA. [PDF]
Quaest Math, 2022 Mansour T +3 more
europepmc +1 more source