cp's OEIS Frontend

A292213 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than seven.

%I A292213 #5 Sep 11 2017 18:45:48
%S A292213 0,1,1,2,5,12,33,90,260,763,2302,7035,21854,68581,217485,695229,
%T A292213 2238965,7255380,23643501,77426852,254678757,841028918,2787320206,
%U A292213 9267764857,30906754731,103350631437,346465277423,1164150100182,3920004155435,13225916804136
%N A292213 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than seven.
%H A292213 Alois P. Heinz, <a href="/A292213/b292213.txt">Table of n, a(n) for n = 0..1000</a>
%H A292213 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%p A292213 b:= proc(n, i, v) option remember; `if`(n=0,
%p A292213       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A292213       `if`(v=n, 1, add(binomial(a(i)+j-1, j)*
%p A292213        b(n-i*j, i-1, v-j), j=0..min(n/i, v)))))
%p A292213     end:
%p A292213 a:= proc(n) option remember; `if`(n<2, n,
%p A292213       add(b(n, n+1-j, j), j=2..min(n, 7)))
%p A292213     end:
%p A292213 seq(a(n), n=0..35);
%Y A292213 Column k=7 of A292085.
%K A292213 nonn
%O A292213 0,4
%A A292213 _Alois P. Heinz_, Sep 11 2017