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A318853 Number of rooted trees with n nodes such that no more than six isomorphic subtrees extend from the same node.

%I A318853 #5 Sep 04 2018 17:33:23
%S A318853 0,1,1,2,4,9,20,48,114,284,714,1829,4731,12391,32711,87083,233347,
%T A318853 629132,1705026,4642964,12696279,34851400,95996673,265251812,
%U A318853 735029389,2042187079,5687726124,15876511622,44409196932,124459720195,349434222059,982723600768
%N A318853 Number of rooted trees with n nodes such that no more than six isomorphic subtrees extend from the same node.
%H A318853 Alois P. Heinz, <a href="/A318853/b318853.txt">Table of n, a(n) for n = 0..2136</a>
%p A318853 h:= proc(n, m, t) option remember; `if`(m=0, binomial(n+t, t),
%p A318853       `if`(n=0, 0, add(h(n-1, m-j, t+1), j=1..min(6, m))))
%p A318853     end:
%p A318853 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318853       add(b(n-i*j, i-1)*h(a(i), j, 0), j=0..n/i)))
%p A318853     end:
%p A318853 a:= n-> `if`(n<2, n, b(n-1$2)):
%p A318853 seq(a(n), n=0..35);
%Y A318853 Column k=6 of A318757.
%K A318853 nonn
%O A318853 0,4
%A A318853 _Alois P. Heinz_, Sep 04 2018