cp's OEIS Frontend

A244706 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 5.

%I A244706 #5 Jul 08 2014 09:02:59
%S A244706 1,1,3,6,15,31,72,153,346,752,1673,3661,8108,17814,39349,86646,191251,
%T A244706 421596,930519,2052789,4531648,10002857,22088709,48780279,107757048,
%U A244706 238069894,526096509,1162775782,2570487392,5683401236,12568472173,27799055016,61496981626
%N A244706 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 5.
%C A244706 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 A244706 Alois P. Heinz, <a href="/A244706/b244706.txt">Table of n, a(n) for n = 6..1000</a>
%p A244706 b:= proc(n, i, h, v) option remember; `if`(n=0,
%p A244706       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A244706       `if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, j)
%p A244706        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))
%p A244706     end:
%p A244706 A:= proc(n, k) option remember;
%p A244706       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k,n-1)))
%p A244706     end:
%p A244706 a:= n-> b(n-1$2, 5$2):
%p A244706 seq(a(n), n=6..50);
%Y A244706 Column k=5 of A244657.
%K A244706 nonn
%O A244706 6,3
%A A244706 _Alois P. Heinz_, Jul 04 2014