a(n) = [x^n] ((x - 1)/sqrt(4/(x + 1) - 3) + x + 1)/(2*x*(3*x - 1)).

Terms

a(0) =0a(1) =1a(2) =6a(3) =26a(4) =100a(5) =361a(6) =1254a(7) =4245a(8) =14108a(9) =46247a(10) =149998a(11) =482412a(12) =1540880a(13) =4893859a(14) =15468910a(15) =48696930a(16) =152764452a(17) =477771447a(18) =1490245302a(19) =4637349186a(20) =14400224496a(21) =44632551567a(22) =138101593398a(23) =426658380621