The number of 1+1+1-free ordered posets of [n].

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =23a(5) =102a(6) =497a(7) =2586a(8) =14127a(9) =80146a(10) =468688a(11) =2810163a(12) =17206549a(13) =107261051a(14) =679096359a(15) =4358360362a(16) =28309516828a(17) =185862601727