a(n) = 2^n * [x^n] Product_{k>=1} ((1 + 2*x^k)/(1 - 2*x^k))^(1/4).

Terms

a(0) =1a(1) =2a(2) =6a(3) =28a(4) =70a(5) =300a(6) =892a(7) =3544a(8) =9990a(9) =43340a(10) =127988a(11) =546120a(12) =1651356a(13) =7227896a(14) =22414008a(15) =99344944a(16) =312879302a(17) =1396285452a(18) =4486205892a(19) =20057934312a(20) =65293087284a(21) =292353604136a(22) =963327294536