19404

Appears in sequences

• a(n) = (2*n)!*(2*n+1)! / (n! * (n+1)!)^2.at n=5A000891
• Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.at n=60A001263
• Number of partitions into one kind of 1's, two kinds of 2's, and three kinds of 3's.at n=41A002597
• a(n) is the number of n-step walks on square lattice such that 0 <= y <= x at each step.at n=10A005558
• a(n) = 7*(n+1)*binomial(n+6,7)/2.at n=5A027819
• a(n) = 42*(n+1)*binomial(n+6,10).at n=2A027822
• Triangle read by rows: T(k,j) = ((2*j+1)/(k+1))*binomial(2*j,j)*binomial(2*k-2*j,k-j).at n=50A033820
• a(n) = Product_{i=1..n} ((i+5)*(i+6)*(i+7)*(i+8)*(i+9))/(i*(i+1)*(i+2)*(i+3)*(i+4)).at n=2A047831
• Positions of 4-digit terms in the continued fraction for Pi (3 is at position 0).at n=17A048959
• Number of antichains (or order ideals) in the poset 5*m*n or plane partitions with not more than m rows, n columns and entries <= 5.at n=30A056941
• Number of antichains (or order ideals) in the poset 5*m*n or plane partitions with not more than m rows, n columns and entries <= 5.at n=33A056941
• Numbers k such that sigma(k^2 + 1) == 0 (mod k).at n=34A067719
• Triangle read by rows: T(n, k) = binomial(2*n+1, n-k)^2*(2*k+1)/(2*n+1).at n=15A067802
• Products of members of pairs in A075333.at n=34A075337
• Table by antidiagonals giving variants on Catalan sequence: T(n,k)=C(2n,n)*C(2k,k)*(2k+1)/(n+k+1).at n=49A078817
• Triangle T(n,k) read by rows, given by [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...] DELTA [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, ...] where DELTA is the operator defined in A084938.at n=59A086329
• Triangle read by rows of the numbers T(n,k) (n > 1, 0 < k < n) of set partitions of n of length k which do not have a proper subset of parts with a union equal to a subset {1,2,...,j} with j < n.at n=51A087903
• Square array T(n,k) read by antidiagonals: number of tilings of an <n,k,n> hexagon.at n=23A103905
• a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)^2*(n+5)^2*(n+6)/86400.at n=5A108679
• Triangle of Dyck paths counted by number of long interior inclines.at n=49A108838