A335748 T(n,k) = (-1)^n*(binomial(2*k,k)/(k+1))*Sum_{j=0..n} (-1)^j*binomial(k,j)*j^n. Triangle read by rows, T(n, k) for n >= 0 and 0 <= k <= n.
1, 0, 1, 0, -1, 4, 0, 1, -12, 30, 0, -1, 28, -180, 336, 0, 1, -60, 750, -3360, 5040, 0, -1, 124, -2700, 21840, -75600, 95040, 0, 1, -252, 9030, -117600, 705600, -1995840, 2162160, 0, -1, 508, -28980, 571536, -5292000, 25280640, -60540480, 57657600
Offset: 0
Examples
[0] 1
[1] 0, 1
[2] 0, -1, 4
[3] 0, 1, -12, 30
[4] 0, -1, 28, -180, 336
[5] 0, 1, -60, 750, -3360, 5040
[6] 0, -1, 124, -2700, 21840, -75600, 95040
[7] 0, 1, -252, 9030, -117600, 705600, -1995840, 2162160
[8] 0, -1, 508, -28980, 571536, -5292000, 25280640, -60540480, 57657600
Crossrefs
Formula
T(n, k) = (-1)^n*CatalanNumber(k)*Sum_{j=0..n}(-1)^j*binomial(k, j)*j^n.