Lah numbers, Laguerre polynomials of order negative one, and the nth derivative of exp(1/x)

[1] J. C. Ahuja, E. A. Enneking, Concavity property and a recurrence relation for associated Lah numbers, Fibonacci Quart., 17 (2) (1979), 158–161.Search in Google Scholar

[2] P. Barry, Some Observations on the Lah and Laguerre Transforms of Integer Sequences, Journal of Integer Sequences, 10 (2007), Article 07.4.6Search in Google Scholar

[3] K. N. Boyadzhiev, Power Series with Binomial Sums and Asymptotic Expansions, Int. Journal of Math. Analysis, 8 (28) (2014), 1389–1414.10.12988/ijma.2014.45126Search in Google Scholar

[4] K. N. Boyadzhiev, Exponential polynomials, Stirling numbers, and evaluation of some Gamma integrals, Abstract and Applied Analysis, Volume 2009, Article ID 168672 (electronic, open source).10.1155/2009/168672Search in Google Scholar

[5] K. N. Boyadzhiev, A Series transformation formula and related polynomials, International Journal of Mathematics and Mathematical Sciences, 2005 (2005), Issue 23, 3849–3866.10.1155/IJMMS.2005.3849Search in Google Scholar

[6] Y. A. Brychkov, Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas, Chapman and Hall/CRC, 2008.10.1201/9781584889571Search in Google Scholar

[7] Charalambos A. Charalambides, Jagbir Singh, A review of the Stirling numbers, their generalizations and statistical interpretations, Comm. Statist. Theory Methods, 17 (8) (1988), 2533–2595.10.1080/03610928808829760Search in Google Scholar

[8] C. A. Charalambides, Enumerative Combinatorics, Chapman and Hall/CRC, 2002.Search in Google Scholar

[9] L. Comtet, Advanced Combinatorics, D. Reidel Publishing Co., Dordrecht, 1974.10.1007/978-94-010-2196-8Search in Google Scholar

[10] S. Daboul, J. Mangaldan, M. Z. Spivey, P. J. Taylor, The Lah Numbers and the nth Derivative of exp(1/x), Math. Magazine, 86 (1) (2013) 39–47.10.4169/math.mag.86.1.039Search in Google Scholar

[11] H. W. Gould, Combinatorial Identities, Published by the author, 1972.Search in Google Scholar

[12] Bai-Ni Guo, F. Qi, Six proofs for an identity of the Lah numbers, Online Journal of Analytic Combinatorics, 10 (2015).Search in Google Scholar

[13] Bai-Ni Guo, F. Qi, Some integral representations and properties of Lah numbers (arxiv.org), 2014.Search in Google Scholar

[14] N. N. Lebedev, Special Functions and Their Applications, Dover, 1972.Search in Google Scholar

[15] F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, 2010.Search in Google Scholar

[16] M. Petkovšek, T. Pisanski, Combinatorial interpretation of unsigned Stirling and Lah numbers, Preprint 40 (2002), Univ. of Ljubljana. (Available on the internet.)Search in Google Scholar

[17] E. D. Rainville, Special Functions, Chelsea, 1971.Search in Google Scholar

[18] I. J. Schwatt, An Introduction to the Operations with Series, Chelsea, 1924.Search in Google Scholar

[19] P. G. Todorov, Taylor expansions of analytic functions related to (1 + z)^x − 1, J. Math. Anal. Appl.,132 (1988), 264–280.10.1016/0022-247X(88)90060-1Search in Google Scholar