Number of partitions of [2n] whose block maxima sum to 3n.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =10a(5) =23a(6) =47a(7) =103a(8) =209a(9) =449a(10) =908a(11) =1909a(12) =3864a(13) =8011a(14) =16165a(15) =33244a(16) =66933a(17) =136628a(18) =274876a(19) =558107a(20) =1121160a(21) =2268526a(22) =4552291a(23) =9183569a(24) =18417449a(25) =37073504a(26) =74300048a(27) =149334422a(28) =299134695a(29) =600481001