a(n) = (1/3)*A099432(n+1).

Terms

a(0) =2a(1) =11a(2) =54a(3) =252a(4) =1134a(5) =4977a(6) =21438a(7) =91017a(8) =381996a(9) =1588248a(10) =6552252a(11) =26853687a(12) =109438938a(13) =443837799a(14) =1792373346a(15) =7211142612a(16) =28915704810a(17) =115603540605a(18) =460942202070