Geodesic
Some classes of numbers and derivatives
Journal of integer sequences, Tome 12 (2009) no. 8
We prove that three classes of numbers -- the non-central Stirling numbers of the first kind, generalized factorial coefficients, and Gould-Hopper numbers -- may be defined by the use of derivatives. We derive several properties of these numbers from their definitions. We also prove a result for harmonic numbers. The coefficients of Hermite and Bessel polynomials are a particular case of generalized factorial coefficients, The coefficients of the associated Laguerre polynomials are a particular case of Gould-Hopper numbers. So we obtain some properties of these polynomials. In particular, we derive an orthogonality relation for the coefficients of Hermite and Bessel polynomials.
Classification : 05A10, 11C08
Keywords: non-central Stirling numbers of the first kind, generalized factorial coefficients, gould-hopper numbers, generalized Stirling numbers 
@article{JIS_2009__12_8_a7,
     author = {Janji\'c,  Milan},
     title = {Some classes of numbers and derivatives},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {8},
     zbl = {1213.05013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_8_a7/}
}
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Janjić,  Milan. Some classes of numbers and derivatives. Journal of integer sequences, Tome 12 (2009) no. 8. http://geodesic.mathdoc.fr/item/JIS_2009__12_8_a7/