johncarlosbaez, 14 days ago (edited 14 days ago) @paulmasson @phonner - as you probably know, Dobiński's formula says [ \displaystyle{ \frac{1}{e} \sum_{k = 0}^\infty \frac{k^n}{k!} = B_n } ] where (B_n) is the nth Bell number. Dobiński published a paper about it in 1877, but it seems that he only proved some special cases. Here I give a combinatorial proof following Gian-Carlo Rota: https://math.ucr.edu/home/baez/permutations/permutations_8.html
@paulmasson @phonner - as you probably know, Dobiński's formula says
[ \displaystyle{ \frac{1}{e} \sum_{k = 0}^\infty \frac{k^n}{k!} = B_n } ]
where (B_n) is the nth Bell number. Dobiński published a paper about it in 1877, but it seems that he only proved some special cases. Here I give a combinatorial proof following Gian-Carlo Rota:
https://math.ucr.edu/home/baez/permutations/permutations_8.html