Geodesic
Asymptotics for Lacunary sums of binomial coefficients and a card problem with ranks
Journal of integer sequences, Tome 10 (2007) no. 7
We find asymptotics for lacunary sums of binomial coefficients. As an application we determine the exact and approximate probability that the first card has the uniquely highest rank among the top $l$ cards of a standard card deck.
Classification : 05A10, 05A16, 11B68
Keywords: lacunary sum, asymptotic enumeration, Bernoulli numbers 
@article{JIS_2007__10_7_a3,
     author = {Lengyel,  Tam\'as},
     title = {Asymptotics for {Lacunary} sums of binomial coefficients and a card problem with ranks},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {7},
     zbl = {1141.05008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_7_a3/}
}
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Lengyel,  Tamás. Asymptotics for Lacunary sums of binomial coefficients and a card problem with ranks. Journal of integer sequences, Tome 10 (2007) no. 7. http://geodesic.mathdoc.fr/item/JIS_2007__10_7_a3/