Number of n-node rooted trees with a forbidden limb of length 8.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =20a(6) =48a(7) =115a(8) =285a(9) =717a(10) =1837a(11) =4753a(12) =12451a(13) =32878a(14) =87549a(15) =234654a(16) =632814a(17) =1715446a(18) =4672544a(19) =12780511a(20) =35091842a(21) =96684570a(22) =267223650a(23) =740691451a(24) =2058470490a(25) =5734620428a(26) =16011730686a(27) =44799543203a(28) =125587727914a(29) =352696990890