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A318798 Number of rooted trees with n nodes such that no more than four subtrees of the same size extend from the same node.

%I A318798 #4 Sep 03 2018 21:07:51
%S A318798 0,1,1,2,4,9,19,46,110,273,684,1746,4503,11758,30943,82118,219337,
%T A318798 589477,1592427,4322386,11781435,32235285,88502260,243747792,
%U A318798 673238061,1864400173,5175591107,14399672901,40146278964,112143682477,313822403439,879673332422
%N A318798 Number of rooted trees with n nodes such that no more than four subtrees of the same size extend from the same node.
%H A318798 Alois P. Heinz, <a href="/A318798/b318798.txt">Table of n, a(n) for n = 0..2143</a>
%p A318798 g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A318798       binomial(g((i-1)$2)+j-1, j)*g(n-i*j, i-1), j=0..min(4, n/i))))
%p A318798     end:
%p A318798 a:= n-> g((n-1)$2):
%p A318798 seq(a(n), n=0..40);
%Y A318798 Column k=4 of A318753.
%K A318798 nonn
%O A318798 0,4
%A A318798 _Alois P. Heinz_, Sep 03 2018