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A245127 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 8.

%I A245127 #8 Jul 12 2014 09:11:10
%S A245127 4,18,75,241,732,2048,5507,14149,35406,86251,206060,483503,1118366,
%T A245127 2553371,5766634,12896468,28598143,62934478,137565845,298871089,
%U A245127 645779488,1388442085,2971788670,6334659311,13452368784,28469327221,60059197787,126331495950,265014539903
%N A245127 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 8.
%H A245127 Alois P. Heinz, <a href="/A245127/b245127.txt">Table of n, a(n) for n = 31..500</a>
%p A245127 b:= proc(n, i, h, v) option remember; `if`(n=0, `if`(v=0, 1, 0),
%p A245127       `if`(i<1 or v<1 or n<v, 0, add(binomial(A(i, min(i-1, h)), j)
%p A245127        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))
%p A245127     end:
%p A245127 A:= proc(n, k) option remember;
%p A245127       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
%p A245127     end:
%p A245127 a:= n-> b(n-1$2, 8$2):
%p A245127 seq(a(n), n=31..65);
%Y A245127 Column k=8 of A245120.
%K A245127 nonn
%O A245127 31,1
%A A245127 _Alois P. Heinz_, Jul 12 2014