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

Terms

a(0) =3a(1) =6a(2) =19a(3) =65a(4) =231a(5) =840a(6) =3102a(7) =11583a(8) =43615a(9) =165308a(10) =629850a(11) =2410226a(12) =9256534a(13) =35659200a(14) =137733660a(15) =533216475a(16) =2068423695a(17) =8037976980a(18) =31285334850a(19) =121941160110a(20) =475898730450