51822

Appears in sequences

• Binomial transform of Catalan numbers.at n=9A007317
• Least nondecreasing sequence with a(1) = 1 and Hankel transform {1,1,1,1,...}.at n=18A055879
• Least nondecreasing sequence with a(1) = 1 and Hankel transform {1,1,1,1,...}.at n=19A055879
• Expansion of (1-3*x+6*x^2-5*x^3+3*x^4-x^5)/(1-x)^6.at n=21A089830
• Triangle read by rows: T(n,k) is the number of Schroeder paths of length 2n and having k peaks at even height.at n=36A101895
• Triangle T read by rows: matrix product of Pascal and Catalan triangle.at n=45A104259
• Sum array of Catalan numbers (A000108) read by upward antidiagonals.at n=45A106534
• Triangle read by rows: T(n,k) (0 <= k <= floor(n/2)) is the number of lattice paths from (0,0) to (2n,0) consisting of steps U=(1,1), D=(1,-1), H=(2,0), never going below the x-axis (i.e., Schroeder paths) and having k UH's.at n=25A110220
• Triangle read by rows: row n is the first row of the matrix M[n]^(n-1), where M[n] is the n X n tridiagonal matrix with main diagonal (2,3,3,...) and super- and subdiagonals (1,1,1,...).at n=45A124733
• Riordan array (1, (1/(1-x))c(x/(1-x))), c(x) the g.f. of A000108.at n=56A155887
• G.f.: (1/2)*(3 - sqrt((1-5*x)/(1-x))).at n=10A181768
• Number of (n+2)X(1+2) 0..3 arrays with every 3X3 subblock row and column sum not 1 3 6 or 8 and every diagonal and antidiagonal sum 1 3 6 or 8.at n=10A252046
• A(n, k) is the n-th binomial transform of the Catalan sequence (A000108) evaluated at k. Array read by descending antidiagonals for n >= 0 and k >= 0.at n=56A271025
• Triangle A106534 with reversed rows.at n=54A280470
• Expansion of Product_{k>=1} (1 + x^k)^(sigma_2(k)).at n=12A288414
• Square array T(m,n) read by antidiagonals, satisfying shifted Catalan recurrences: T(m,0) = 1 and T(m,n) = Sum_{k=0..n-1} T(m,k) * T(m,(n-1-k+m) mod n) for all n > 0.at n=76A341359
• Number of branching factorizations of the least integer of each prime signature (A025487).at n=39A366884
• Number of integer compositions of n whose leaders of maximal weakly increasing runs are not weakly decreasing.at n=18A374636