Arises in enumeration of 321-hexagon-avoiding permutations.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =5a(7) =19a(8) =68a(9) =240a(10) =839a(11) =2911a(12) =10054a(13) =34641a(14) =119203a(15) =409893a(16) =1408873a(17) =4841373a(18) =16634350a(19) =57149111a(20) =196333312a(21) =674477710a(22) =2317047808a(23) =7959739375a(24) =27343914410a(25) =93933688630a(26) =322686958885