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A318857 Number of rooted trees with n nodes such that no more than ten isomorphic subtrees extend from the same node.

%I A318857 #7 Sep 04 2018 18:12:00
%S A318857 0,1,1,2,4,9,20,48,115,286,719,1842,4765,12484,32968,87798,235346,
%T A318857 634752,1720897,4687949,12824195,35216118,97039045,268237121,
%U A318857 743594937,2066803841,5758576675,16080698759,44998355630,126161517745,354354779794,996963790045,2809334906744,7928088014833,22404525682620
%N A318857 Number of rooted trees with n nodes such that no more than ten isomorphic subtrees extend from the same node.
%C A318857 This differs from A318804 first at n=34.
%H A318857 Alois P. Heinz, <a href="/A318857/b318857.txt">Table of n, a(n) for n = 0..2136</a>
%p A318857 h:= proc(n, m, t) option remember; `if`(m=0, binomial(n+t, t),
%p A318857       `if`(n=0, 0, add(h(n-1, m-j, t+1), j=1..min(10, m))))
%p A318857     end:
%p A318857 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318857       add(b(n-i*j, i-1)*h(a(i), j, 0), j=0..n/i)))
%p A318857     end:
%p A318857 a:= n-> `if`(n<2, n, b(n-1$2)):
%p A318857 seq(a(n), n=0..35);
%Y A318857 Column k=10 of A318757.
%Y A318857 Cf. A318804.
%K A318857 nonn
%O A318857 0,4
%A A318857 _Alois P. Heinz_, Sep 04 2018