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

Terms

a(0) =1a(1) =1a(2) =3a(3) =13a(4) =55a(5) =231a(6) =981a(7) =4222a(8) =18351a(9) =80320a(10) =353453a(11) =1562364a(12) =6932185a(13) =30856541a(14) =137725710a(15) =616190583a(16) =2762605791a(17) =12408541299a(18) =55825435656a(19) =251523510045