OFFSET
0,6
FORMULA
T(n, k) = (-1)^n*CatalanNumber(k)*Sum_{j=0..n}(-1)^j*binomial(k, j)*j^n.
EXAMPLE
[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
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Jul 09 2020
STATUS
approved