1767263190

Appears in sequences

• Symmetrical dissections of an n-gon.at n=36A000063
• Catalan numbers with odd index: a(n) = binomial(4*n+2, 2*n+1)/(2*n+2).at n=9A024492
• a(n) = T(n, floor(n/2)), where T = Catalan triangle (A008315).at n=36A026008
• a(n) = floor( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).at n=38A028303
• a(n) = ceiling( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).at n=38A028304
• Largest squarefree number dividing central binomial coefficient A000984(n).at n=19A080397
• a(1) = 1; a(n) = floor {(n+1)(n+2)(n+3)...(n+k)}/{(n-1)(n-2)(n-3)...(n-k)} for the least value of k.at n=19A092935
• Numerators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk.at n=18A093526
• Expansion of 1 + 2x/(1 + sqrt(1 - 4x^2)).at n=39A097331
• Second column and subdiagonal of number triangle A098509.at n=19A098512
• An inverse Chebyshev transform of 1-x.at n=38A099363
• An inverse Chebyshev transform of (1-x)^2.at n=36A099364
• Expansion of 1-x*c(-x^2) where c(x) is the g.f. of A000108.at n=39A105523
• G.f. is 1 + x*c(x), where c(x) is the g.f. of the Catalan numbers (A000108).at n=20A120588
• Catalan numbers (A000108) interpolated with 0's.at n=38A126120
• a(2n) = Cat(n), a(2n+1) = 3*Cat(n), where Cat(n) = binomial(2n,n)/(n+1) are the Catalan numbers (A000108).at n=38A126324
• The matrix-vector product A133566 * A000108.at n=19A133603
• Late-growing permutations: number of permutations of 19 indistinguishable copies of 1..n with every partial sum <= the same partial sum averaged over all permutations.at n=1A147769
• Even Catalan numbers.at n=14A152670
• Number of Dyck paths of semilength n with a valley (DU) spanning the midpoint.at n=19A186031