cp's OEIS Frontend

A292212 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than six.

%I A292212 #5 Sep 11 2017 18:18:39
%S A292212 0,1,1,2,5,12,33,89,258,756,2279,6957,21592,67689,214451,684850,
%T A292212 2203384,7133042,23222003,75971636,249646198,823597534,2726859943,
%U A292212 9057797752,30176758016,100810029178,337614951216,1133292965615,3812333876764,12849946139206
%N A292212 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than six.
%H A292212 Alois P. Heinz, <a href="/A292212/b292212.txt">Table of n, a(n) for n = 0..1000</a>
%H A292212 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%p A292212 b:= proc(n, i, v) option remember; `if`(n=0,
%p A292212       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A292212       `if`(v=n, 1, add(binomial(a(i)+j-1, j)*
%p A292212        b(n-i*j, i-1, v-j), j=0..min(n/i, v)))))
%p A292212     end:
%p A292212 a:= proc(n) option remember; `if`(n<2, n,
%p A292212       add(b(n, n+1-j, j), j=2..min(n, 6)))
%p A292212     end:
%p A292212 seq(a(n), n=0..35);
%Y A292212 Column k=6 of A292085.
%K A292212 nonn
%O A292212 0,4
%A A292212 _Alois P. Heinz_, Sep 11 2017