Triangle of number of permutations by barycenter.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =4a(5) =1a(6) =1a(7) =4a(8) =14a(9) =4a(10) =1a(11) =1a(12) =5a(13) =31a(14) =46a(15) =31a(16) =5a(17) =1a(18) =1a(19) =6a(20) =66a(21) =146a(22) =282a(23) =146a(24) =66a(25) =6a(26) =1a(27) =1a(28) =7a(29) =134