a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 3^k * a(k) * a(n-2*k-1).

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =7a(5) =19a(6) =40a(7) =178a(8) =379a(9) =1237a(10) =2941a(11) =10378a(12) =24628a(13) =78928a(14) =198820a(15) =813550a(16) =1971907a(17) =6587245a(18) =16980079a(19) =61488286a(20) =155573011a(21) =515316037a(22) =1363261084a(23) =4937498686a(24) =12796438252a(25) =42078038668a(26) =113153315824a(27) =390012381346