90440

Appears in sequences

• Fourth convolution of Catalan numbers: a(n) = 4*binomial(2*n+3,n)/(n+4).at n=9A002057
• An inverse Chebyshev transform of x^3.at n=10A099376
• 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=21A101461
• Table (read by rows) giving the coefficients of sum formulas of n-th Factorials (A000142). The k-th row (k>=1, n>=2) contains T(i,k) for i=1 to k+1, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies Fact(n) = Sum_{i=1..k+1} T(i,k) * (n-1)^(k-i+1) / (2*k-2)!.at n=14A101751
• Even triangle n!. This table read by rows gives the coefficients of sum formulas of n-th factorials (A000142). The k-th row (6>=k>=1) contains T(i,k) for i=1 to k+3, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies n! = Sum_{i=1..k+3} T(i,k) * n^(i-1) / (2*k-2)!.at n=28A102409
• a(n) = binomial(n,4) - binomial(floor(n/2),4) - binomial(ceiling(n/2),4).at n=41A111385
• 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=38A114494
• 10th column of Catalan triangle A009766.at n=3A124088
• a(n) = Fibonacci(n)*A109064(n) for n>=1 with a(0)=1.at n=18A205882
• Number of (n+5) X 1 arrays of occupancy after each element moves up to +-5 places including 0.at n=4A222342
• T(n,k)=Number of length (n+k)X1 arrays of occupancy after each element moves up to +-k places including 0.at n=40A222345
• Number of (n+5)X1 arrays of occupancy after each element moves up to +-n places including 0.at n=4A222349
• Number of ballot sequences of length n having 9 largest parts.at n=12A244106
• Triangle, read by rows, T(n,k) = 2*k*C(2*(n+k),n-k)/(n+k).at n=45A257501
• Cayley's triangle of V numbers; triangle V(n,k), n >= 4, n <= k <= 2*n-4, read by rows.at n=54A259476
• Square table where T(n,k) = binomial(n*(n+k), k) * n/(n+k), for n>=1, k>=0, as read by antidiagonals.at n=63A299427
• Arises from enumeration of a certain class of partial zig-zag knight's paths on the square grid.at n=20A368378