A068338 n!^2 * sum{k=1 to n} mu(k)/k^2, where mu(k) is the Moebius function.

1, 3, 23, 368, 8624, 324864, 15399936, 985595904, 79833268224, 8115008716800, 968747865292800, 139499692602163200, 23346005516963020800, 4614592869368384716800, 1045883450064438558720000