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A318854 Number of rooted trees with n nodes such that no more than seven isomorphic subtrees extend from the same node.

%I A318854 #5 Sep 04 2018 17:41:42
%S A318854 0,1,1,2,4,9,20,48,115,285,717,1837,4753,12451,32878,87549,234654,
%T A318854 632813,1715444,4672539,12780498,35091807,96684475,267223388,
%U A318854 740690724,2058468456,5734614714,16011714554,44799497491,125587597952,352696620393,992168348175
%N A318854 Number of rooted trees with n nodes such that no more than seven isomorphic subtrees extend from the same node.
%H A318854 Alois P. Heinz, <a href="/A318854/b318854.txt">Table of n, a(n) for n = 0..2136</a>
%p A318854 h:= proc(n, m, t) option remember; `if`(m=0, binomial(n+t, t),
%p A318854       `if`(n=0, 0, add(h(n-1, m-j, t+1), j=1..min(7, m))))
%p A318854     end:
%p A318854 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318854       add(b(n-i*j, i-1)*h(a(i), j, 0), j=0..n/i)))
%p A318854     end:
%p A318854 a:= n-> `if`(n<2, n, b(n-1$2)):
%p A318854 seq(a(n), n=0..35);
%Y A318854 Column k=7 of A318757.
%K A318854 nonn
%O A318854 0,4
%A A318854 _Alois P. Heinz_, Sep 04 2018