a(n) = hypergeom([-n/3, (1 - n)/3, (2 - n)/3], [1, 1], -27).

Terms

a(0) =1a(1) =1a(2) =1a(3) =7a(4) =25a(5) =61a(6) =211a(7) =841a(8) =2857a(9) =9745a(10) =36421a(11) =134971a(12) =488731a(13) =1807807a(14) =6788965a(15) =25384087a(16) =95114377a(17) =359291737a(18) =1361265889a(19) =5162682775a(20) =19642369405a(21) =74960720065a(22) =286563664135