%I #7 Sep 12 2017 11:54:04
%S 1,2,7,22,72,230,751,2442,8006,26280,86604,285994,946866,3140812,
%T 10438300,34747649,115849084,386779317,1292998720,4327654320,
%U 14500841169,48639319376,163308287353,548820437392,1845999502151,6214297279692,20935992503127,70586182742450
%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals four.
%H Alois P. Heinz, <a href="/A292230/b292230.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%e : a(6) = 7:
%e : o o o o
%e : / \ / \ /( )\ / | \
%e : o N o N o N N N o N N
%e : / \ /( )\ / \ /( )\
%e : o N o N N N o N N N N N
%e : /( )\ ( ) ( )
%e : N N N N N N N N
%e :
%e : o o o
%e : / \ /( )\ / ( \ \
%e : o o o N N N o o N N
%e : /( )\ ( ) /|\ ( ) ( )
%e : N N N N N N N N N N N N N
%e :
%p b:= proc(n, i, v, k) option remember; `if`(n=0,
%p `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p `if`(v=n, 1, add(binomial(A(i, k)+j-1, j)*
%p b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))
%p end:
%p A:= proc(n, k) option remember; `if`(n<2, n,
%p add(b(n, n+1-j, j, k), j=2..min(n, k)))
%p end:
%p a:= n-> A(n, 4)-A(n, 3):
%p seq(a(n), n=4..35);
%Y Column k=4 of A292086.
%K nonn
%O 4,2
%A _Alois P. Heinz_, Sep 12 2017