The Entringer Number E(n, k) are the number of permutations of {1, 2, …, n + 1}, starting with k + 1, which, after initally falling, alternatively fall then rise. The Entringer are given by:
E(n,k) = 0 if k == 0
= 1 if k == 0 and n == 0
= E(n,k-1) + E(n-1 , n-k) otherwise