Dobinski's formula, published by G. Dobinski in 1877, expresses the nth Bell number, which counts the partitions of a set of size n, as an infinite series: the sum over all natural numbers k of k raised to the nth power divided by k factorial, with the whole sum then divided by Euler's number e. The formula gives a direct analytic route to the Bell numbers even though the underlying combinatorial quantity is purely discrete.
Facts
StatementDobinski's formula states that the nth Bell number Bn, the number of partitions of a set of size n, equals the sum from k=0 to infinity of k to the n over k factorial, divided by e. 1 Classification
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Source Dobinski's formula (Wikipedia)
Sources
1. Dobinski's formula (Wikipedia)
Introduction
Dobiński's formula states that the n th Bell number B n , the number of partitions of a set of size n , equals
Lead section
The formula is named after G. Dobiński, who published it in 1877.
In Branch: Combinatorics, Lead
In combinatorial mathematics, Dobiński's formula states that the
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