246675

Appears in sequences

• a(n) = binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees).at n=9A001764
• a(n) = floor( binomial(n,8)/9).at n=27A011845
• Number of necklaces with 9 black beads and n-9 white beads.at n=19A032194
• Schoenheim bound L_1(n,9,8).at n=18A036836
• If n = 2*m then a(n) = binomial(3*m, m)/(2*m+1), if n=2*m+1 then a(n) = binomial(3*m+1, m+1)/(2*m+1).at n=18A047749
• Number of dissectable polyhedra with n tetrahedral cells and symmetry of type I.at n=72A047753
• Number of dissectable polyhedra with n tetrahedral cells and symmetry of type F.at n=34A047760
• a(n) = A047760(2n+1).at n=17A047761
• Number of dissectable polyhedra with n tetrahedral cells and symmetry of type P.at n=35A047765
• a(n) = A047765(2n).at n=17A047767
• Number of dissectable polyhedra with n tetrahedral cells and symmetry of type D.at n=54A047773
• a(n) = ceiling(binomial(n,9)/n).at n=27A053733
• Triangle read by rows: T(n,k) = binomial(3n+3, k)*(n-k+1)/(n+1).at n=44A064282
• Second level generalization of Catalan triangle (0th level is Pascal's triangle A007318; first level is Catalan triangle A009766; 3rd level is A069270).at n=54A069269
• Denominator of 2*Sum(C(n,w)/(2*w+1),w=0..n/2-1)+C(n,n/2)/(n+1) if n is even, or of 2*Sum(C(n,w)/(2*w+1),w=0..(n-1)/2) if n is odd.at n=38A085569
• Triangle of coefficients, read by rows, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/(1-x) - x^2/(1-x)^3 + xy*f(x,y)^3.at n=54A086632
• Triangle of coefficients, read by rows, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = (1+x) - x^2*(1+x)^3 + xy*f(x,y)^3.at n=54A086634
• Triangle read by rows: T(n,k) (n >= 2, k >= 0) is the number of non-crossing connected graphs on n nodes on a circle, having k interior faces. Rows are indexed 2,3,4,...; columns are indexed 0,1,2,....at n=36A089434
• Triangle read by rows: T(n,k) is the number of noncrossing forests with n vertices and k components (1<=k<=n).at n=45A094021
• Triangle read by rows: T(n,k) is the number of noncrossing forests with n vertices and k edges.at n=54A094040