101042

Appears in sequences

• Number of alternating permutations of order n.at n=10A001250
• Read across rows of Euler-Bernoulli or Entringer triangle.at n=37A008283
• Triangle read by rows: number of permutations of 1..n by length of longest run.at n=44A010026
• Twice A000364.at n=5A011248
• Triangle read by rows: T(n,k) is the number of permutations of [n] with k alternating runs (n>=2, k>=1).at n=44A059427
• Numbers n such that n''' = n''+ 1 where n'' and n''' are respectively the second and the third arithmetic derivative of n.at n=22A189941
• Triangle read by rows: number of permutations of 1..n by length l of longest run (n >= 1, 1 <= l <= n).at n=46A211318
• T(n,k) = number of permutations of {1..n} with fewer than k interior elements having values lying between the values of their neighbors.at n=54A226441
• T(n,k) = number of arrays of length n that are sums of k consecutive elements of length n+k-1 permutations of 0..n+k-2, and no two consecutive rises or falls in the latter permutation.at n=54A229717
• Twice the Euler or up/down numbers A000111.at n=10A260786
• Number T(n,k) of permutations of [n] with exactly k (possibly overlapping) occurrences of the consecutive step patterns 010 or 101, where 1=up and 0=down; triangle T(n,k), n >= 0, k = max(0, n-3), read by rows.at n=38A295987
• Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. (sec(x) + tan(x))^k.at n=75A322267