175032

Appears in sequences

• Number of tree-rooted bridgeless planar maps with two vertices and n faces.at n=10A002740
• Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by the n-th Catalan number (A000108).at n=47A085880
• Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by the n-th Catalan number (A000108).at n=52A085880
• Array read by rows: T(n,k) = binomial(n+k-2,k-1)*binomial(2*n-1,n-k).at n=37A091811
• Product of Pell and Catalan numbers: a(n) = A000129(n+1)*A000108(n).at n=7A098616
• Triangle read by rows: T(n,k)=2^k*binomial(2n-k,n-k), 1<=k<=n.at n=46A112326
• Expansion of c(x*y(1+x)), c(x) the g.f. of A000108.at n=75A117434
• Number of polygons on n vertices with exactly three faces.at n=9A128650
• Number of ways to place zero or more nonadjacent 0,0 1,0 1,1 2,0 2,2 3,0 3,1 3,2 polyhexes in any orientation on a planar nXnXn triangular grid.at n=9A155360
• Number of 6-step self-avoiding walks on an n X n square summed over all starting positions.at n=26A188151
• Number of (w,x,y,z) with all terms in {1,...,n} and w<=2x and y>3z.at n=35A212514
• The Wiener index of the Kneser graph K(n,2) (n>=5).at n=29A228306
• Number of ways to place 2 points on a triangular grid of side n so that they are not adjacent.at n=32A239568
• Number T(n,k) of 2n-length strings of balanced parentheses of exactly k different types that are introduced in ascending order; triangle T(n,k), n>=0, 0<=k<=n, read by rows.at n=53A253180
• Number of 2n-length strings of balanced parentheses of exactly 8 different types that are introduced in ascending order.at n=1A258396
• Starting a random walk on Z at 0 triangle T(j,k) gives the number of paths of length 2*j returning to 0 exactly k times.at n=57A276418
• G.f. C(x)^(1/2) satisfies C(x)^(1/2) - S(x)^(1/2) = 1 such that C'(x)*S(x)^(1/2) = S'(x)*C(x)^(1/2) = 72*x.at n=7A299855
• Triangle read by rows, interpolating between the central binomial coefficients and the central coefficients of the Catalan triangle. T(n, k) for 0 <= k <= n.at n=37A330798
• T(n, k) = (k*(2*k+2)*(2*k+1)*(2*n-1)*binomial(2*(n-1),n-1))/(n*(n+1)*(n+2)) for n, k > 0 and T(0, 0) = 1. Triangle read by rows, for 0 <= k <= n.at n=44A337994
• Triangle read by rows: T(n,k) is the number of tree-rooted planar maps with n edges, k faces and no isthmuses, n >= 0, k = 1..n+1.at n=53A342987