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A292229 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals three.

%I A292229 #10 Sep 12 2017 11:53:42
%S A292229 1,2,6,17,47,133,380,1096,3186,9351,27618,82168,245882,740003,2238186,
%T A292229 6801375,20754977,63583715,195486605,603003882,1865692570,5788676649,
%U A292229 18007192835,56151236196,175486946089,549586009252,1724530420457,5421195811358,17070958403725
%N A292229 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals three.
%H A292229 Alois P. Heinz, <a href="/A292229/b292229.txt">Table of n, a(n) for n = 3..1000</a>
%H A292229 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%e A292229 : a(5) = 6:
%e A292229 :        o        o        o        o          o         o
%e A292229 :       / \      / \      /|\     /   \       /|\      / | \
%e A292229 :      o   N    o   N    o N N   o     o     o N N   o   o  N
%e A292229 :     / \      /|\      / \     /|\   ( )   /|\     ( ) ( )
%e A292229 :    o   N    o N N    o   N   N N N  N N  N N N    N N N N
%e A292229 :   /|\      ( )      ( )
%e A292229 :  N N N     N N      N N
%e A292229 :
%p A292229 b:= proc(n, i, v, k) option remember; `if`(n=0,
%p A292229       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A292229       `if`(v=n, 1, add(binomial(A(i, k)+j-1, j)*
%p A292229        b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))
%p A292229     end:
%p A292229 A:= proc(n, k) option remember; `if`(n<2, n,
%p A292229       add(b(n, n+1-j, j, k), j=2..min(n, k)))
%p A292229     end:
%p A292229 a:= n-> A(n, 3)-A(n, 2):
%p A292229 seq(a(n), n=3..35);
%Y A292229 Column k=3 of A292086.
%K A292229 nonn
%O A292229 3,2
%A A292229 _Alois P. Heinz_, Sep 12 2017