Triangle of scaled second column sequences of (k,k)-Stirling2 arrays.

Terms

a(0) =1a(1) =3a(2) =1a(3) =7a(4) =8a(5) =1a(6) =15a(7) =52a(8) =30a(9) =1a(10) =31a(11) =320a(12) =756a(13) =144a(14) =1a(15) =63a(16) =1936a(17) =18360a(18) =17856a(19) =840a(20) =1a(21) =127a(22) =11648a(23) =441936a(24) =2156544a(25) =619200a(26) =5760a(27) =1a(28) =255a(29) =69952