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A318800 Number of rooted trees with n nodes such that no more than six subtrees of the same size extend from the same node.

%I A318800 #4 Sep 03 2018 21:47:52
%S A318800 0,1,1,2,4,9,20,48,114,284,714,1829,4731,12391,32711,87083,233347,
%T A318800 629132,1705026,4642964,12696279,34851400,95996667,265251800,
%U A318800 735029359,2042187008,5687725928,15876511087,44409195451,124459715968,349434210318,982723567822
%N A318800 Number of rooted trees with n nodes such that no more than six subtrees of the same size extend from the same node.
%H A318800 Alois P. Heinz, <a href="/A318800/b318800.txt">Table of n, a(n) for n = 0..2136</a>
%p A318800 g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A318800       binomial(g((i-1)$2)+j-1, j)*g(n-i*j, i-1), j=0..min(6, n/i))))
%p A318800     end:
%p A318800 a:= n-> g((n-1)$2):
%p A318800 seq(a(n), n=0..40);
%Y A318800 Column k=6 of A318753.
%K A318800 nonn
%O A318800 0,4
%A A318800 _Alois P. Heinz_, Sep 03 2018