cp's OEIS Frontend

A292234 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals eight.

%I A292234 #6 Sep 12 2017 11:55:28
%S A292234 1,2,7,23,78,262,893,3039,10405,35692,122807,423392,1462748,5061942,
%T A292234 17544791,60893535,211610421,736189821,2563823467,8937012397,
%U A292234 31179543205,108865543805,380389514123,1330027798273,4653356214277,16290208735442,57059113819218
%N A292234 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals eight.
%H A292234 Alois P. Heinz, <a href="/A292234/b292234.txt">Table of n, a(n) for n = 8..1000</a>
%H A292234 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%p A292234 b:= proc(n, i, v, k) option remember; `if`(n=0,
%p A292234       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A292234       `if`(v=n, 1, add(binomial(A(i, k)+j-1, j)*
%p A292234        b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))
%p A292234     end:
%p A292234 A:= proc(n, k) option remember; `if`(n<2, n,
%p A292234       add(b(n, n+1-j, j, k), j=2..min(n, k)))
%p A292234     end:
%p A292234 a:= n-> A(n, 8)-A(n, 7):
%p A292234 seq(a(n), n=8..35);
%Y A292234 Column k=8 of A292086.
%K A292234 nonn
%O A292234 8,2
%A A292234 _Alois P. Heinz_, Sep 12 2017