a(n) is the number of cyclic permutations with at most 2 ascents.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =6a(5) =18a(6) =58a(7) =186a(8) =570a(9) =1680a(10) =4878a(11) =14058a(12) =40200a(13) =114450a(14) =325290a(15) =923846a(16) =2624730a(17) =7465410a(18) =21261828a(19) =60647370a(20) =173288724a(21) =496014934a(22) =1422223506a(23) =4084793082a(24) =11751102060a(25) =33857989968a(26) =97697014590a(27) =282295318536a(28) =816759712080