432073

Properties

Appears in sequences

• a(n) = Sum_{k=0..n-1} binomial(n-1,k)*binomial(n+k,k). Also a(n) = T(n,n), array T as in A049600.at n=9A047781
• a(n) = n*(2*n^8 + 84*n^6 + 798*n^4 + 1636*n^2 + 315)/2835.at n=9A099196
• Triangle read by rows: T(n,k) is the number of bicolored Dyck paths of semilength n and having k peaks of the form ud (0 <= k <= n). A bicolored Dyck path is a Dyck path in which each up-step is of two kinds: u and U.at n=46A114608
• a(1)=433640083; a(n+1)= the largest prime factor of a(n)+b(n)+c(n), where a(n)<b(n)<c(n) and a(n),b(n) and c(n) are three consecutive primes.at n=8A117631
• Number of paths from (0,0) to the line x = n, each segment given by a vector (1,1), (1,-1), or (2,0), not crossing the x-axis, and including no horizontal segment on the x-axis.at n=17A247623
• Array read by antidiagonals: the number of directed elements with area n on the lattice T_{2k+1}.at n=56A296129
• Triangle read by rows, T(n, k) = (-1)^(n-k)*binomial(n,k)*hypergeom([k - n, n + 1], k + 1, 2), for n >= 0 and 0 <= k <= n.at n=46A297898
• Crystal ball sequence for the lattice C_9.at n=4A305723
• Prime numbersat n=36327