Number of permutations of [n] having exactly three adjacent 3-cycles.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =0a(7) =0a(8) =0a(9) =1a(10) =4a(11) =20a(12) =116a(13) =820a(14) =6600a(15) =59650a(16) =598140a(17) =6592740a(18) =79232140a(19) =1031214100a(20) =14450182880a(21) =216911207555