Answer by Math1000 for Need Help with Mistake in Generating Function for...
Multiplying both sides of the recurrence by $x^n$ and summing for $n=2$ to infinity:$$\sum_{n=2}^\infty w_nx^n = \sum_{n=2}^\infty \sum_{k=1}^{n-1} w_kw_{n-k}x^n + \sum_{n=2}^\infty x^n.$$Because...
View ArticleNeed Help with Mistake in Generating Function for Nonlinear Recurrence relation
I'm having a bit of trouble finding the generating function for the following recurrence relation:$$w_n -1 = \sum _{k=1}^{n-1} w_k w_{n-k}, \quad n \geq 2, \; w_0 = 0, \; w_1 = 1.$$I set out to find a...
View Article
More Pages to Explore .....
