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Eulerian numbers

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1: 26.14 Permutations: Order Notation
The Eulerian number, denoted n k , is the number of permutations in 𝔖 n with exactly k descents. …
Table 26.14.1: Eulerian numbers n k .
n k
26.14.8 n k = ( k + 1 ) n - 1 k + ( n - k ) n - 1 k - 1 , n 2 ,
26.14.9 n k = n n - 1 - k , n 1 ,
26.14.14 n 0 = 1 ,
2: 26.1 Special Notation
( m n )

binomial coefficient.

m n

Eulerian number.

3: 24.4 Basic Properties
§24.4(ix) Relations to Other Functions
For the relation of Bernoulli numbers to the Riemann zeta function see §25.6, and to the Eulerian numbers see (26.14.11).
4: Bibliography C
  • L. Carlitz (1954a) q -Bernoulli and Eulerian numbers. Trans. Amer. Math. Soc. 76 (2), pp. 332–350.