Number T(n,k) of permutations on n elements with exactly k 3-cycles; triangle read by rows.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =2a(5) =16a(6) =8a(7) =80a(8) =40a(9) =520a(10) =160a(11) =40a(12) =3640a(13) =1120a(14) =280a(15) =29120a(16) =8960a(17) =2240a(18) =259840a(19) =87360a(20) =13440a(21) =2240a(22) =2598400a(23) =873600a(24) =134400a(25) =22400a(26) =28582400a(27) =9609600a(28) =1478400a(29) =246400