a(n) = [x^n] 2/(3*x + sqrt((1 - 3*x)*(x + 1)) + 1).

Terms

a(0) =1a(1) =-1a(2) =2a(3) =-2a(4) =5a(5) =-3a(6) =15a(7) =3a(8) =59a(9) =73a(10) =308a(11) =632a(12) =1951a(13) =4829a(14) =13674a(15) =36306a(16) =100827a(17) =275493a(18) =765150a(19) =2120466a(20) =5918943a(21) =16547595a(22) =46452387a(23) =130703031a(24) =368825661a(25) =1043125407a(26) =2957013140a(27) =8399389528a(28) =23904802109a(29) =68154435941