Asymptotics of Some Convolutional Recurrences

作者：Bender Edward A^*; Olde Daalhuis Adri B; Gao Zhicheng; Richmond L Bruce; Wormald Nicholas

来源：Electronic Journal of Combinatorics, 2010, 17(1): R1.

We study the asymptotic behavior of the terms in sequences satisfying recurrences of the form a(n)=a(n-1) + Sigma(n-d)(k=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 Painleve I equations are discussed in detail.

• 出版日期2010-1-5