The subsequence A253069(2^n-1).

Terms

a(0) =1a(1) =6a(2) =22a(3) =82a(4) =302a(5) =1106a(6) =4066a(7) =14902a(8) =54678a(9) =200578a(10) =735770a(11) =2699182a(12) =9901550a(13) =36323050a(14) =133247570a(15) =488805718a(16) =1793137798a(17) =6577952882a(18) =24130592458a(19) =88520767614a(20) =324729961566