Summation Properties
It is clear from the combinatoric definition that the sum of the Eulerian numbers for a fixed value of n is the total number of permutations of the numbers 1 to n, so
The alternating sum of the Eulerian numbers for a fixed value of n is related to the Bernoulli number Bn+1
Other summation properties of the Eulerian numbers are:
where Bn is the nth Bernoulli number.
Read more about this topic: Eulerian Number
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