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A318852 Number of rooted trees with n nodes such that no more than five isomorphic subtrees extend from the same node.

%I A318852 #5 Sep 04 2018 17:24:13
%S A318852 0,1,1,2,4,9,20,47,113,281,706,1807,4671,12223,32245,85777,229670,
%T A318852 618732,1675523,4559000,12456756,34166545,94034740,259621512,
%U A318852 718846854,1995610386,5553500697,15489256677,43290763753,121226491459,340079258393,955634312429
%N A318852 Number of rooted trees with n nodes such that no more than five isomorphic subtrees extend from the same node.
%H A318852 Alois P. Heinz, <a href="/A318852/b318852.txt">Table of n, a(n) for n = 0..2138</a>
%p A318852 h:= proc(n, m, t) option remember; `if`(m=0, binomial(n+t, t),
%p A318852       `if`(n=0, 0, add(h(n-1, m-j, t+1), j=1..min(5, m))))
%p A318852     end:
%p A318852 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318852       add(b(n-i*j, i-1)*h(a(i), j, 0), j=0..n/i)))
%p A318852     end:
%p A318852 a:= n-> `if`(n<2, n, b(n-1$2)):
%p A318852 seq(a(n), n=0..35);
%Y A318852 Column k=5 of A318757.
%K A318852 nonn
%O A318852 0,4
%A A318852 _Alois P. Heinz_, Sep 04 2018