Number of series-reduced rooted trees whose leaves form an integer partition of n with no 1's.

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =2a(5) =5a(6) =6a(7) =15a(8) =22a(9) =51a(10) =86a(11) =195a(12) =354a(13) =781a(14) =1512a(15) =3286a(16) =6602a(17) =14269a(18) =29424a(19) =63494a(20) =133298a(21) =287909a(22) =612188a(23) =1325375a(24) =2844448a(25) =6176145a(26) =13348858a(27) =29074164a(28) =63187176a(29) =138044144