Journal of Integer Sequences, Vol. 17 (2014), Article 14.10.6

Linear Recurrences for r-Bell Polynomials


Miloud Mihoubi and Hacène Belbachir
USTHB, Faculty of Mathematics RECITS Laboratory, DG-RSDT
P. O. Box 32
16111 El-Alia
Bab-Ezzouar
Algiers
Algeria

Abstract:

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}\} _{i}$ and $ \{ xB_{i}( 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 $\mathbb{Q} $-vector space formed by polynomials of $\mathbb{Q} [X].$

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(Concerned with sequences A000110.)

Received November 3 2013; revised version received January 19 2014; January 29 2014; July 20 2014; September 6 2014; September 10 2014. Published in Journal of Integer Sequences, November 5 2014.

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