78592

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=8A047781
• Convolution of A055854 with A011782.at n=8A055855
• a(n) = n^2*(n^6 + 28*n^4 + 154*n^2 + 132)/315.at n=8A099195
• 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=37A114608
• a(n) = 2*a(n-2) + 4*a(n-3), with initial terms 0, 1, 1.at n=18A134136
• a(n) = AlexanderPolynomial[n] defined as Det[Transpose[S]-n S] where S is Kronecker Product of two 2 X 2 Seifert matrices {{-1, 1}, {0, -1}} [X] {{-1, 1}, {0, -1}} = {{1, -1, -1, 1}, {0, 1, 0, -1}, {0, 0, 1, -1}, {0, 0, 0, 1}}.at n=17A138849
• 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=15A247623
• Array read by antidiagonals: the number of directed elements with area n on the lattice T_{2k+1}.at n=46A296129
• 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=37A297898