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.
|Number of pages||11|
|Journal||Electronic Journal of Combinatorics|
|Publication status||Published - 5 Jan 2010|
- 1ST PAINLEVE EQUATION
- RICCATI EQUATION
- NONLINEAR ODES
- WIENER INDEX