a(n) = L(2*n+1) - 2, where L is A000032.

Terms

a(0) =-1a(1) =2a(2) =9a(3) =27a(4) =74a(5) =197a(6) =519a(7) =1362a(8) =3569a(9) =9347a(10) =24474a(11) =64077a(12) =167759a(13) =439202a(14) =1149849a(15) =3010347a(16) =7881194a(17) =20633237a(18) =54018519a(19) =141422322a(20) =370248449a(21) =969323027a(22) =2537720634a(23) =6643838877a(24) =17393795999a(25) =45537549122a(26) =119218851369a(27) =312119004987a(28) =817138163594