175502

Appears in sequences

• Generalized Catalan numbers: a(n+1) = a(n) + Sum_{k=1..n-1} a(k)*a(n-1-k).at n=17A004148
• Essentially same as A004148.at n=18A025241
• 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=51A182896
• Number of elevated peakless Motzkin paths.at n=19A203019
• Number of 3X3X3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and every horizontal row having the same average value.at n=38A214541
• Number of (n+2) X (1+2) 0..1 arrays with each 3 X 3 subblock having clockwise perimeter pattern 00000101 00010001 or 00010101.at n=12A260602
• Expansion of (1 - x - x^2 - sqrt((1 - x - x^2)^2 - 4*x^3))/(2*x^3) in powers of x.at n=16A292460