The first 30 terms of the sequence enumerating reduced super Latin 3 by n rec\
    tangles (i.e. 3 by n matrices whose first row is 1,...,n, the second and\
     third row are permutations of {1,..,n}

   all the columns are distict and all diagonals of size 3 are distinct are

[0, 0, 0, 0, 2, 46, 1536, 96956, 8011672, 845786038, 107815737778, 
16296369840412, 2874882373259026, 585093479946815912, 136056344787943685846, 
35852908253977226957738, 10629400014719465666082692, 
3522806448573524827144616160, 1297684073470554414905615877716, 
528562474513580488000178047915604, 236933054568182241403215751592914832, 
116383616407496110435262852399109650496, 
62400368123172654648119506092531788674782, 
36386660860725044394844994349201833951753396, 
22999058097725895449804349056246299359042450608, 
15709144812817996707660523784826639669740858315334, 
11561885404424724504475328353273662754687184479666326, 
9145015359308785725518520375973006505071897357982086232, 
7754329230484600091683515209428738703961891536296964063604, 
7032392635743259863975634396890394404268105322058722906743606]


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