41586

Appears in sequences

• Large Schröder numbers (or large Schroeder numbers, or big Schroeder numbers).at n=8A006318
• a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-2)*a(2) for n >= 3.at n=8A025240
• Triangular array read by rows associated with Schroeder numbers: T(1,k) = 1; T(n,k) = 0 if k < n; T(n,k) = T(n,k-1) + T(n-1,k-1) + T(n-1,k).at n=44A033877
• Triangular array associated with Schroeder numbers.at n=54A033878
• Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(1,0)=2, a(n,0)=A006318(n), a(n,n)=A006319(n), a(n+1,0)=a(n,0)+a(n,n), a(n,m+1)= Sum A006318(k)*a(n-k,0), k=0..m.at n=36A073150
• Inverse of coordination sequence array A113413.at n=36A080245
• Formal inverse of triangle A080246. Unsigned version of A080245.at n=36A080247
• Square array T(n,d) read by antidiagonals: number of structurally-different guillotine partitions of a d-dimensional box in R^d by n hyperplanes.at n=37A103209
• Triangular array associated with Schroeder numbers: T(0,0) = 1, T(n,0) = 0 for n > 0; T(n,k) = 0 if k < n; T(n,k) = T(n,k-1) + T(n-1,k-1) + T(n-1,k).at n=54A106579
• Number array whose rows are the series reversions of x(1-x)/(1+x)^k, read by antidiagonals.at n=53A107111
• Triangle related to guillotine partitions of a k-dimensional box by n hyperplanes.at n=53A107702
• Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and have k peaks (i.e., ud and Ud's).at n=35A108425
• Triangle read by rows: T(n,k) = number of Schroeder (or royal) n-paths (A006318) containing k returns to the diagonal y=x. (A northeast step lying on y=x contributes a return.)at n=36A108891
• Triangle read by rows: T(n,k) (0 <= k <= n) is the number of Delannoy paths of length n, having k return steps to the line y = x from the line y = x+1 (i.e., E steps from the line y=x+1 to the line y = x).at n=36A110098
• Triangle read by rows: T(n,k) (0<=k<=n) is the number of Delannoy paths of length n, having k (1,1)-steps on the lines y=x, y=x+1 and y=x-1.at n=36A110183
• Triangle read by rows: T(n,k) (0<=k<=n) is the number of Schroeder paths of length 2n, having k (1,0)-steps on the lines y=0 and y=1 (a Schroeder path of length 2n is a path from (0,0) to (2n,0), consisting of steps U=(1,1), D=(1,-1) and H=(2,0) and never going below the x-axis).at n=45A110189
• Riordan array ((1-x+sqrt(1+6*x+x^2))/2, (sqrt(1+6*x+x^2)-x-1)/2).at n=45A112477
• Expansion of (1 + x + sqrt(1 + 6*x + x^2))/2.at n=9A112478
• Riordan array (1, x*f(x)) where f(x)is the g.f. of A006318.at n=46A122538
• T(n, k) counts Schroeder n-paths whose ascent starting at the initial vertex has length k. Triangle T(n,k), read by rows.at n=45A132372