Eulerian Number

In combinatorics, the Eulerian Number E(n, m), is the number of permutations of the numbers 1 to n in which exactly m elements are greater than previous element.

Recurrence Relation

      E(m,n)  =   0                                                     if(m >= n || n == 0) 
      E(m,n)  =   1                                                     if (m == 0) 
      E(m,n)  =   (n - m) * E(n - 1, m - 1) +  m + 1) * E(n - 1, m)     otherwise

Input : n = 3, m = 1
Output : 4
Please see above diagram (There
are 4 permutations where 1 no. is
greater.

Input : n = 4, m = 1
Output : 11