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A245124 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 5.

%I A245124 #8 Jul 12 2014 08:15:25
%S A245124 1,4,11,28,70,160,366,804,1748,3734,7918,16597,34601,71628,147631,
%T A245124 302857,619231,1261849,2564795,5200248,10522565,21252174,42854194,
%U A245124 86286963,173517189,348523105,699311092,1401837776,2807733181,5619221464,11238041122,22460777472
%N A245124 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 5.
%H A245124 Alois P. Heinz, <a href="/A245124/b245124.txt">Table of n, a(n) for n = 15..750</a>
%e A245124 a(15) = 1:
%e A245124 :        o        :
%e A245124 :   / (  |  ) \   :
%e A245124 :  o  o  o  o  o  :
%e A245124 :  | ( ) |  |     :
%e A245124 :  o o o o  o     :
%e A245124 :  | |   |        :
%e A245124 :  o o   o        :
%e A245124 :  |              :
%e A245124 :  o              :
%p A245124 b:= proc(n, i, h, v) option remember; `if`(n=0, `if`(v=0, 1, 0),
%p A245124       `if`(i<1 or v<1 or n<v, 0, add(binomial(A(i, min(i-1, h)), j)
%p A245124        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))
%p A245124     end:
%p A245124 A:= proc(n, k) option remember;
%p A245124       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
%p A245124     end:
%p A245124 a:= n-> b(n-1$2, 5$2):
%p A245124 seq(a(n), n=15..50);
%Y A245124 Column k=5 of A245120.
%K A245124 nonn
%O A245124 15,2
%A A245124 _Alois P. Heinz_, Jul 12 2014