72832

Appears in sequences

• Generalized Catalan numbers: a(n+1) = a(n) + Sum_{k=1..n-1} a(k)*a(n-1-k).at n=16A004148
• Essentially same as A004148.at n=17A025241
• Multiplicity of highest weight (or singular) vectors associated with character chi_170 of Monster module.at n=41A034558
• Numbers in A086473 corresponding to the unique product of two numbers having the unique sum of A086533.at n=23A086860
• Triangle read by rows: T(n,k) is the number of Motzkin paths of length n with k valleys (n>=0, 0<=k<=floor(n/2)-1; a valley is a downstep followed by an upstep).at n=51A097885
• Triangle, read by rows, equal to P^4, where triangle P = A135880; also equals Q^2, where triangle Q = P^2 = A135885.at n=22A135891
• Triangle read by rows: T(n,k) is the number of weighted lattice paths in L_n having k (1,-1)-returns to the horizontal axis. The members of L_n are paths of weight n that start at (0,0), end on the horizontal axis and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps.at n=45A182896
• Number of elevated peakless Motzkin paths.at n=18A203019
• Non-crossing, non-nesting, 4-colored permutations on {1,2,...,n}.at n=5A224993
• Expansion of (1 - x - x^2 - sqrt((1 - x - x^2)^2 - 4*x^3))/(2*x^3) in powers of x.at n=15A292460