Mihoubi, Miloud Bell polynomials and binomial type sequences. (English) Zbl 1147.05006 Discrete Math. 308, No. 12, 2450-2459 (2008). Summary: This paper concerns the study of the Bell polynomials and the binomial type sequences. We mainly establish some relations tied to these important concepts. Furthermore, these obtained results are exploited to deduce some interesting relations concerning the Bell polynomials which enable us to obtain some new identities for the Bell polynomials. Our results are illustrated by some comprehensive examples. Cited in 1 ReviewCited in 28 Documents MSC: 05A15 Exact enumeration problems, generating functions 05A10 Factorials, binomial coefficients, combinatorial functions 05A19 Combinatorial identities, bijective combinatorics 11B73 Bell and Stirling numbers 11B83 Special sequences and polynomials Keywords:Bell polynomials; binomial type sequences; generating function; identities PDFBibTeX XMLCite \textit{M. Mihoubi}, Discrete Math. 308, No. 12, 2450--2459 (2008; Zbl 1147.05006) Full Text: DOI References: [1] M. Aigner, Combinatorial Theory, Springer, Berlin, Heidelberg, New York, 1979, pp. 99-116.; M. Aigner, Combinatorial Theory, Springer, Berlin, Heidelberg, New York, 1979, pp. 99-116. [2] Abbas, M.; Bouroubi, S., On new identities for Bell’s polynomials, Discrete Math., 293, 5-10 (2005) · Zbl 1063.05014 [3] Bell, E. T., Exponential polynomials, Ann. Math., 35, 258-277 (1934) · JFM 60.0295.01 [4] Bernardini, A.; Ricci, P. E., Bell polynomials and differential equations of Freud-type polynomials, Math. Comput. Modelling, 36, 9/10, 1115-1119 (2002) · Zbl 1029.33003 [5] C. Cassisa, P.E. Ricci, Orthogonal invariants and the Bell polynomials, Rendiconti di Matematica, Serie VII, vol. 20, Roma, 2000, pp. 293-303.; C. Cassisa, P.E. Ricci, Orthogonal invariants and the Bell polynomials, Rendiconti di Matematica, Serie VII, vol. 20, Roma, 2000, pp. 293-303. · Zbl 1005.47027 [6] Collins, C. B., The role of Bell polynomials in Integration, J. Comput. Appl. Math., 131, 195-222 (2001) · Zbl 0992.65011 [7] L. Comtet, Advanced Combinatorics. D. Reidel Publishing Company, Dordrecht-Holland, Boston-USA, 1974, pp. 133-175.; L. Comtet, Advanced Combinatorics. D. Reidel Publishing Company, Dordrecht-Holland, Boston-USA, 1974, pp. 133-175. [8] L. Comtet, Analyse Combinatoire, Collection SUP, Presse Universitaire de France, 1970.; L. Comtet, Analyse Combinatoire, Collection SUP, Presse Universitaire de France, 1970. [9] Isoni, T.; Natalini, P.; Ricci, P. E., Symbolic computation of Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators, Numer. Algorithms Special Volume in Memory of W. Gross, 28, 1-4, 215-227 (2001) · Zbl 0997.65102 [10] Kirschenhofer, P., An alternating sum, Electron. J. Combinatorics, 3, 2, #R7 (1996) [11] Riordan, J., Combinatorial Identities (1968), Wiley: Wiley New York · Zbl 0194.00502 [12] Riordan, J., An Introduction to Combinatorial Analysis (1953), Wiley: Wiley New York, Chichester [13] Roman, S., The Umbral Calculus (1984), Academic Press Inc: Academic Press Inc New York · Zbl 0536.33001 [14] Zeng, J., Multinomial convolution polynomials, Discrete Math., 160, 219-228 (1996) · Zbl 0860.05005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.