Values of n such that Sum[ -(-1)^(k) n/k (n-1)/(k+1),{k,1,n}] (n!!) is an integer.

Terms

a(0) =1a(1) =5a(2) =9a(3) =11a(4) =13a(5) =17a(6) =25a(7) =33a(8) =49a(9) =65a(10) =97a(11) =129a(12) =193a(13) =257a(14) =385a(15) =513a(16) =769a(17) =1025a(18) =1537a(19) =2049a(20) =3073a(21) =4097a(22) =6145a(23) =8193a(24) =12289a(25) =16385a(26) =24577a(27) =32769a(28) =49153a(29) =65537