a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n+k,n-3*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =21a(5) =76a(6) =226a(7) =680a(8) =2269a(9) =7915a(10) =27136a(11) =91246a(12) =307374a(13) =1047619a(14) =3595866a(15) =12352159a(16) =42415949a(17) =145850821a(18) =502698331a(19) =1735954780a(20) =6001926436a(21) =20770641161a(22) =71951921108a(23) =249507459224a(24) =866031978142