Estimating a cumulative sum

This article derives an asymptotic formula for the cumulative sum of the number of unlabeled rooted trees (OEIS A000081), denoted c(n), which also counts constraints on n-step Runge-Kutta methods. The author uses the known asymptotic estimate for t(n) and assumes the cumulative sum of asymptotics gives an asymptotic for the cumulative sum, justified by rapid growth. The result is c(n) ~ C * α^(n+1) * n^(-3/2) / (α - 1). The article includes Python code using matplotlib to plot the ratio of exact values to the approximation, demonstrating convergence. The technique is generalizable to other rapidly growing sequences with known asymptotics.