@article{Klazar:JCT:2003,
    Abstract = {We prove that the ordinary generating function of Bell numbers satisfies no algebraic differential equation over C(x) (in fact, over a larger field). We investigate related numbers counting various set partitions (the Uppuluri--Carpenter numbers, the numbers of partitions with jmodi blocks, the Bessel numbers, the numbers of connected partitions, and the numbers of crossing partitions) and prove for their ogf's analogous results. Recurrences, functional equations, and continued fraction expansions are derived.},
    Author = {Klazar, Martin},
    File = {Bell numbers, their relatives, and algebraicdifferential equations - 1-s2.0-S0097316503000141-main - a - a.pdf},
    ISSN = {0097-3165},
    Journal = {Journal of Combinatorial Theory, Series A},
    Keywords = {Bell number, Ordinary generating function, Algebraic differential equation, Set partition, Continued fraction, Crossing},
    Number = {1},
    Pages = {63--87},
    Title = {Bell numbers, their relatives, and algebraic differential equations},
    URL = {http://www.sciencedirect.com/science/article/pii/S0097316503000141},
    Volume = {102},
    Year = {2003},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0097316503000141},
    bdsk-url-2 = {https://doi.org/10.1016/S0097-3165(03)00014-1},
    date-added = {2020-09-30 18:56:21 +0200},
    date-modified = {2020-09-30 18:56:53 +0200},
    doi = {10.1016/S0097-3165(03)00014-1}
}

@article{Klazar:JCT:2003, Abstract = {We prove that the ordinary generating function of Bell numbers satisfies no algebraic differential equation over C(x) (in fact, over a larger field). We investigate related numbers counting various set partitions (the Uppuluri--Carpenter numbers, the numbers of partitions with jmodi blocks, the Bessel numbers, the numbers of connected partitions, and the numbers of crossing partitions) and prove for their ogf's analogous results. Recurrences, functional equations, and continued fraction expansions are derived.}, Author = {Klazar, Martin}, File = {Bell numbers, their relatives, and algebraicdifferential equations - 1-s2.0-S0097316503000141-main - a - a.pdf}, ISSN = {0097-3165}, Journal = {Journal of Combinatorial Theory, Series A}, Keywords = {Bell number, Ordinary generating function, Algebraic differential equation, Set partition, Continued fraction, Crossing}, Number = {1}, Pages = {63--87}, Title = {Bell numbers, their relatives, and algebraic differential equations}, URL = {http://www.sciencedirect.com/science/article/pii/S0097316503000141}, Volume = {102}, Year = {2003}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0097316503000141}, bdsk-url-2 = {https://doi.org/10.1016/S0097-3165(03)00014-1}, date-added = {2020-09-30 18:56:21 +0200}, date-modified = {2020-09-30 18:56:53 +0200}, doi = {10.1016/S0097-3165(03)00014-1} }