A245127 - OEIS

%I #8 Jul 12 2014 09:11:10

%S 4,18,75,241,732,2048,5507,14149,35406,86251,206060,483503,1118366,

%T 2553371,5766634,12896468,28598143,62934478,137565845,298871089,

%U 645779488,1388442085,2971788670,6334659311,13452368784,28469327221,60059197787,126331495950,265014539903

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

%H Alois P. Heinz, <a href="/A245127/b245127.txt">Table of n, a(n) for n = 31..500</a>

%p b:= proc(n, i, h, v) option remember; `if`(n=0, `if`(v=0, 1, 0),

%p       `if`(i<1 or v<1 or n<v, 0, add(binomial(A(i, min(i-1, h)), j)

%p        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))

%p     end:

%p A:= proc(n, k) option remember;

%p       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))

%p     end:

%p a:= n-> b(n-1$2, 8$2):

%p seq(a(n), n=31..65);

%Y Column k=8 of A245120.

%K nonn

%O 31,1

%A _Alois P. Heinz_, Jul 12 2014