cp's OEIS Frontend

A318802 Number of rooted trees with n nodes such that no more than eight subtrees of the same size extend from the same node.

%I A318802 #4 Sep 03 2018 22:12:19
%S A318802 0,1,1,2,4,9,20,48,115,286,718,1840,4761,12473,32938,87716,235119,
%T A318802 634120,1719126,4682961,12810091,35176098,96925138,267912073,
%U A318802 742665243,2064139425,5750927105,16058701943,44935012264,125978876147,353827545177,995440198738
%N A318802 Number of rooted trees with n nodes such that no more than eight subtrees of the same size extend from the same node.
%H A318802 Alois P. Heinz, <a href="/A318802/b318802.txt">Table of n, a(n) for n = 0..2136</a>
%p A318802 g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A318802       binomial(g((i-1)$2)+j-1, j)*g(n-i*j, i-1), j=0..min(8, n/i))))
%p A318802     end:
%p A318802 a:= n-> g((n-1)$2):
%p A318802 seq(a(n), n=0..40);
%Y A318802 Column k=8 of A318753.
%K A318802 nonn
%O A318802 0,4
%A A318802 _Alois P. Heinz_, Sep 03 2018