Triangle of number of node labeled trees by number of nodes and number of labels.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =2a(7) =4a(8) =9a(9) =16a(10) =3a(11) =9a(12) =26a(13) =67a(14) =125a(15) =6a(16) =20a(17) =75a(18) =251a(19) =680a(20) =1296a(21) =11a(22) =48a(23) =214a(24) =888a(25) =3135a(26) =8716a(27) =16807a(28) =23a(29) =115