a(n) = Sum_{k=0..n} binomial(2*n+3*k,n-k).

Terms

a(0) =1a(1) =3a(2) =14a(3) =69a(4) =344a(5) =1721a(6) =8621a(7) =43206a(8) =216570a(9) =1085574a(10) =5441294a(11) =27272044a(12) =136679882a(13) =684959516a(14) =3432431414a(15) =17199626276a(16) =86182614207a(17) =431824008713