326876

Appears in sequences

• Fourth convolution of Catalan numbers: a(n) = 4*binomial(2*n+3,n)/(n+4).at n=10A002057
• Number of permutations of [n+1] with exactly 1 increasing subsequence of length 3.at n=9A003517
• a(n) = floor(binomial(n,10)/10).at n=25A011856
• Number of ways to place a non-attacking white and black king on n X n chessboard.at n=23A035286
• Number of nonnegative integer 4 X 4 matrices with sum of elements equal to n, up to rotational symmetry.at n=9A054773
• Triangle T(n,k) read by rows: permutations on 123...n with one abc pattern and no aj pattern with j<=k, n>2, k<n-1.at n=45A084249
• An inverse Chebyshev transform of x^3.at n=11A099376
• Row maximum of Catalan triangle with zeros (A053121), i.e., maximum value of (m+1)*binomial(n+1,(n-m)/2)/(n+1) for given n with m same parity as n.at n=23A101461
• Triangle read by rows: T(n,k) is number of hill-free Dyck paths of semilength n and having k returns to the x-axis. (A Dyck path is said to be hill-free if it has no peaks at level 1.)at n=44A114494
• Triangle read by rows: T(n,k) is the number of Grand Dyck paths of semilength n that cross downwards the x-axis k times. (A Grand Dyck path of semilength n is a path in the half-plane x>=0, starting at (0,0), ending at (2n,0) and consisting of steps u=(1,1) and d=(1,-1)).at n=37A118919
• 10th column of Catalan triangle A009766.at n=5A124088
• Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (6,n)-rectangular grid with k '1's and (6n-k) '0's: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.at n=49A228165
• Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (6,n)-rectangular grid with k '1's and (6n-k) '0's: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.at n=55A228165
• Number of ballot sequences of length n having 9 largest parts.at n=14A244106
• Number of ballot sequences of length n having 10 largest parts.at n=13A244107
• Cayley's triangle of V numbers; triangle V(n,k), n >= 4, n <= k <= 2*n-4, read by rows.at n=65A259476
• a(n) is the common difference of the increasing arithmetic progression C(m,k), C(m,k+1), C(m,k+2) when C(m,k) = A349736(n).at n=2A349737
• Arises from enumeration of a certain class of partial zig-zag knight's paths on the square grid.at n=22A368378
• Arises from enumeration of a certain class of partial zig-zag knight's paths on the square grid.at n=22A368379