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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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What is the exact asymptotic bound on the following sum of polynomials?
I am trying to describe the asymptotic growth of the function $$f(n) = \sum_{k = 1}^{n-1} \frac{k^{2n - 4k - 3}(n^2 -2nk + 2k^2)}{(n-k)^{2n-4k-1}}$$ as $n \rightarrow \infty$. Plotting $f(n)$ for the …