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Tagged with bell-numbers limits
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Relation between Bell number and $F(n)$ the number of partitions of $[n]$ without singeton blocks
Let $F(n)$ be the number of all partitions of $[n]$ with no singleton blocks.
Prove that
$$\lim_{n\to\infty}\frac{F(n)}{B(n)}=0$$
According to this question, we can know
$$F(n+1)=\sum_{i=0}^{n-1}(-1)^...
- 153
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On the ratio $\frac{F_n}{B_n}$
One of the interesting limits that I came up with is:
$$\lim_{n\to\infty} \frac{F_{n}}{B_{n}}\;\;\;\;\;\;\;\;\;\; \left( n \in \mathbb N^+\right)$$
Where $F_n$ is the nth Fibonacci number and $B_n$...
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