a(n) = binomial(2*n-1, n) - binomial(2*n-1, n+3).

Terms

a(0) =1a(1) =3a(2) =10a(3) =34a(4) =117a(5) =407a(6) =1430a(7) =5070a(8) =18122a(9) =65246a(10) =236436a(11) =861764a(12) =3157325a(13) =11622015a(14) =42961470a(15) =159419670a(16) =593636670a(17) =2217608250a(18) =8308432140a(19) =31212003420a(20) =117544456770a(21) =443690433654