2620708

Appears in sequences

• Triangle, read by rows, T(n, k) = 2*A123125(n-1, k), for n >= 2, otherwise T(n, 0) = T(n, n) = -1, with T(0, 0) = T(1, 0) = 1.at n=71A141591
• Triangle, read by rows, T(n, k) = 2*A123125(n-1, k), for n >= 2, otherwise T(n, 0) = T(n, n) = -1, with T(0, 0) = T(1, 0) = 1.at n=72A141591
• Eulerian version of the Catalan numbers, a(n) = A008292(2*n+1,n+1)/(n+1).at n=5A177042
• Number of permutations p of [n] such that the sequence of ascents and descents of p or of p0 (if n is even) forms a Dyck path.at n=11A303287
• Number T(n,k) of permutations of {0,1,...,2n} with first element k whose sequence of ascents and descents forms a Dyck path; triangle T(n,k), n>=0, 0<=k<=2n, read by rows.at n=47A316728
• Number T(n,k) of permutations p of [n] with exactly k descents such that the up-down signature of p has nonnegative partial sums; triangle T(n,k), n>=0, 0<=k<=max(0,floor((n-1)/2)), read by rows.at n=36A321280