151008

Appears in sequences

• a(n) = Product_{1<=i<=j<=n} (i+j+n-1)/(i+j-1), number of symmetric plane partitions in n-cube.at n=5A049505
• Triangle of numbers of square lattice walks that start and end at origin after 2k steps and contain exactly r steps to the east, not touching origin at intermediate stages.at n=37A068218
• Triangle T(n,k) read by rows: related to David G. Cantor's sigma function.at n=60A073165
• Square array T(n,k) read by antidiagonals: T(n,k) = Product_{1<=i<=j<=k} (n+i+j-1)/(i+j-1).at n=40A102539
• Triangular array, read by rows, associated with sums of certain Vandermonde determinants.at n=49A133112
• Dimensions of certain Lie algebra (see reference for precise definition).at n=5A133348
• Triangular array of generalized Narayana numbers: T(n, k) = 4*binomial(n+1, k+3)*binomial(n+1, k-1)/(n+1).at n=48A145598
• a(n) = Sum_{k=0..n} binomial(n+k+2,k)*binomial(2*n+1,n-k).at n=6A275827
• Maximum number of copies of a 123456 permutation pattern in an alternating (or zig-zag) permutation of length n + 9.at n=17A339356
• Averages k of twin prime pairs such that A075255(k) is also the average of a twin prime pair.at n=21A340570
• a(n) is the number of singleton commuting ordered set partitions.at n=8A376544
• Triangle read by rows: T(n, k) is the number of walks of length 2*n on the N X N grid with unit steps in all four directions (NSWE) starting at (0, 0). k is the common value of the x- and the y-coordinate of the endpoint of the walk.at n=22A380119