3362260

Appears in sequences

• Number of dissections of a polygon: binomial(4*n, n)/(3*n + 1).at n=9A002293
• a(n) = floor( binomial(n,8)/9).at n=36A011845
• Number of necklaces with 9 black beads and n-9 white beads.at n=28A032194
• a(n) = ceiling(binomial(n,9)/n).at n=36A053733
• Third level generalization of Catalan triangle (0th level is Pascal's triangle A007318; first level is Catalan triangle A009766; 2nd level is A069269).at n=54A069270
• Length of lists created by n substitutions k -> Range[k+1,1,-3] starting with {1}, counting down from k+1 to 1 step -3.at n=26A084080
• a(n) = (4/(n + 1)) * C(5*n, n).at n=7A124724
• a(3n+k) = (k+1)*binomial(4n+k, n)/(3n+k+1), where k is n reduced mod 3.at n=27A124753
• Triangle of Generalized Runyon numbers R_{n,k}^(4) read by rows.at n=44A173621
• Triangle T(n,m) read by rows, obtained from [A(x)]^m = Sum_{n>=m} T(n,m)*x^n, where A(x) (the g.f. for A069271) satisfies 2*x^2*A(x)^3 = 1 - 2*x*A(x) - sqrt(1-4*x*A(x)).at n=46A188108
• Array t(n,k) = binomial(n*k, n+1)/n, where n >= 1 and k >= 2, read by ascending antidiagonals.at n=48A241262
• Triangle read by rows: the x = 1+q Narayana triangle at m=3.at n=36A243661
• Triangle read by rows: the reversed x = 1+q Narayana triangle at m=3.at n=36A243663
• Number of aperiodic necklaces (Lyndon words) with 9 black beads and n white beads.at n=28A263318
• The Fuss-Catalan triangle of order 3, read by rows. Related to quartic trees.at n=54A355174
• Expansion of g.f. A(x,y) satisfying y/x = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (A(x,y)^(3*n) - 1/A(x,y)^(3*n+1)), as a triangle read by rows.at n=54A361050
• Expansion of g.f. A(x) satisfying A(x) = 1 + x*(3*A(x)^2 + A(-x)^2)/4.at n=18A369082
• Number of achiral polyominoes composed of n pentagonal cells of the hyperbolic regular tiling with Schläfli symbol {5,oo}.at n=17A369472
• Number of subsets of 9 integers between 1 and n such that their sum is 3 modulo n.at n=27A381351