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A244705 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 4.

%I A244705 #5 Jul 08 2014 09:00:33
%S A244705 1,1,3,6,15,29,68,140,312,660,1443,3084,6710,14425,31278,67508,146300,
%T A244705 316424,685955,1486008,3223480,6992012,15179437,32960891,71617874,
%U A244705 155661971,338508703,736401503,1602712182,3489454243,7600403101,16560519877,36097320801
%N A244705 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 4.
%C A244705 In a rooted tree with thinning limbs the outdegree of a parent node is larger than or equal to the outdegree of any of its child nodes.
%H A244705 Alois P. Heinz, <a href="/A244705/b244705.txt">Table of n, a(n) for n = 5..1000</a>
%p A244705 b:= proc(n, i, h, v) option remember; `if`(n=0,
%p A244705       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A244705       `if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, j)
%p A244705        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))
%p A244705     end:
%p A244705 A:= proc(n, k) option remember;
%p A244705       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k,n-1)))
%p A244705     end:
%p A244705 a:= n-> b(n-1$2, 4$2):
%p A244705 seq(a(n), n=5..50);
%Y A244705 Column k=4 of A244657.
%K A244705 nonn
%O A244705 5,3
%A A244705 _Alois P. Heinz_, Jul 04 2014