Arises in enumeration of 321-hexagon-avoiding permutations.

Terms

a(0) =0a(1) =0a(2) =1a(3) =4a(4) =14a(5) =48a(6) =165a(7) =568a(8) =1954a(9) =6717a(10) =23082a(11) =79307a(12) =272470a(13) =936065a(14) =3215741a(15) =11047122a(16) =37950140a(17) =130369334a(18) =447853808a(19) =1538496047a(20) =5285135093a(21) =18155807539a(22) =62369881206a(23) =214256590058a(24) =736026444181