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How to solve a complex recursive relation
Before I get started, let me say for complete disclosure this question came up while I was solving a problem from https://projecteuler.net/.I've been trying to find a non-recursive representation of...
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With $S(0)=0$ one has$$S(n)=-\sum_{k=1}^n\frac{F_k}{k!}$$where $F_k$ are the Fubini numbers (also known as ordered Bell numbers). The proof is contained in my comments above, given that the exponential...
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