Arises in combinatorial approach to the power of 2 in the number of involutions.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =6a(6) =8a(7) =26a(8) =41a(9) =145a(10) =253a(11) =978a(12) =1858a(13) =7726a(14) =15796a(15) =69878a(16) =152219a(17) =711243a(18) =1638323a(19) =8039510a(20) =19467494a(21) =99862594a(22) =252998224a(23) =1351486758a(24) =3568259503a(25) =19786100599a(26) =54263159347a(27) =311482467134a(28) =884834059454