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%I #8 Jul 12 2014 08:15:25
%S 1,4,11,28,70,160,366,804,1748,3734,7918,16597,34601,71628,147631,
%T 302857,619231,1261849,2564795,5200248,10522565,21252174,42854194,
%U 86286963,173517189,348523105,699311092,1401837776,2807733181,5619221464,11238041122,22460777472
%N Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 5.
%H Alois P. Heinz, <a href="/A245124/b245124.txt">Table of n, a(n) for n = 15..750</a>
%e a(15) = 1:
%e : o :
%e : / ( | ) \ :
%e : o o o o o :
%e : | ( ) | | :
%e : o o o o o :
%e : | | | :
%e : o o o :
%e : | :
%e : o :
%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, 5$2):
%p seq(a(n), n=15..50);
%Y Column k=5 of A245120.
%K nonn
%O 15,2
%A _Alois P. Heinz_, Jul 12 2014
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