Number of nonisomorphic ordered triples of involutions on a (2n)-set that pairwise commute.

Terms

a(0) =1a(1) =8a(2) =43a(3) =176a(4) =611a(5) =1864a(6) =5161a(7) =13184a(8) =31532a(9) =71264a(10) =153444a(11) =316608a(12) =629236a(13) =1209312a(14) =2255324a(15) =4093056a(16) =7246690a(17) =12542736a(18) =21262582a(19) =35359456a(20) =57767766a(21) =92832784a(22) =146908290a(23) =229169792a(24) =352721676a(25) =536076640a(26) =805132548a(27) =1195771840a(28) =1757278132