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%I #4 Sep 05 2018 11:53:05
%S 1,1,3,8,22,60,167,464,1302,3666,10370,29421,83736,238891,683088,
%T 1956968,5616281,16142818,46463814,133903792,386336345,1115804329,
%U 3225691950,9333321576,27027053245,78322024353,227126864470,659069928758,1913612752613,5559288014180
%N Number of n-node rooted trees in which seven equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.
%H Alois P. Heinz, <a href="/A318903/b318903.txt">Table of n, a(n) for n = 7..2137</a>
%p g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
%p `if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
%p end:
%p a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(7):
%p seq(a(n), n=7..37);
%Y Column k=7 of A255704.
%K nonn
%O 7,3
%A _Alois P. Heinz_, Sep 05 2018
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