Geodesic
Asymptotics of some convolutional recurrences
The electronic journal of combinatorics, Tome 17 (2010)
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We study the asymptotic behavior of the terms in sequences satisfying recurrences of the form $a_n = a_{n-1} + \sum_{k=d}^{n-d} f(n,k) a_k a_{n-k}$ where, very roughly speaking, $f(n,k)$ behaves like a product of reciprocals of binomial coefficients. Some examples of such sequences from map enumerations, Airy constants, and Painlevé I equations are discussed in detail.
DOI : 10.37236/273
Classification : 05A16, 05A10, 39A20 
@article{10_37236_273,
     author = {Edward A. Bender and Adri B. Olde Daalhuis and Zhicheng Gao and L. Bruce Richmond and Nicholas Wormald},
     title = {Asymptotics of some convolutional recurrences},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/273},
     zbl = {1193.05018},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/273/}
}
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Edward A. Bender; Adri B. Olde Daalhuis; Zhicheng Gao; L. Bruce Richmond; Nicholas Wormald. Asymptotics of some convolutional recurrences. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/273

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