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Jun 21, 2023 at 15:18 comment added Michael Hardy @IraGessel : Rota shows no sign of being aware of the Robbins lemma.
Jun 21, 2023 at 15:17 comment added Michael Hardy @IraGessel : Rota cites a paper of a person named Dobinski (and I think there's a diacritic missing from that spelling, although that is how Rota spelled it) that gives a formula that amounts to saying it's the expected value of the $n$th power of a Poisson-distributed random variable whose 1st power has expected value $1,$ but Rota doesn't mention the Poisson distribution. (But he did later.) Dobinski's paper appeared in 1877.
Jun 21, 2023 at 15:11 comment added Michael Hardy @IraGessel : I don't know. Rota wrote "The earliest occurrence in print of these numbers has never been traced; as expected, the numbers have been attributed to Euler, but an explicit reference to Euler has not been given, and Bell doubts that it can be found in Euler's work." Rota mentions Eric Temple Bell and Jacques Touchard among those who have written about this sequence of numbers. The papers by Bell and Touchard that he cites are from the 1930s and the 1950s.
Jun 20, 2023 at 21:42 history edited Michael Hardy CC BY-SA 4.0
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Jun 20, 2023 at 19:00 comment added Ira Gessel So who was the first to study them?
Jun 20, 2023 at 17:06 history edited Michael Hardy CC BY-SA 4.0
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S Jun 20, 2023 at 16:53 history answered Michael Hardy CC BY-SA 4.0
S Jun 20, 2023 at 16:53 history made wiki Post Made Community Wiki by Michael Hardy