cp's OEIS Frontend

A248890 Number of rooted trees with n nodes such that for each inner node no more than k subtrees corresponding to its children have exactly k nodes.

%I A248890 #10 Feb 28 2017 12:08:20
%S A248890 0,1,1,1,2,4,8,16,34,75,166,374,849,1952,4522,10566,24840,58760,
%T A248890 139693,333702,800412,1927207,4655997,11283835,27423930,66825194,
%U A248890 163227234,399587270,980222058,2409181633,5931839530,14629639579,36137308192,89395224033
%N A248890 Number of rooted trees with n nodes such that for each inner node no more than k subtrees corresponding to its children have exactly k nodes.
%H A248890 Alois P. Heinz, <a href="/A248890/b248890.txt">Table of n, a(n) for n = 0..1000</a>
%e A248890 :  o  :  o  :  o  :    o   o  :    o     o     o   o  :
%e A248890 :     :  |  :  |  :   / \  |  :    |    / \   / \  |  :
%e A248890 :     :  o  :  o  :  o   o o  :    o   o   o o   o o  :
%e A248890 :     :     :  |  :  |     |  :   / \  |     |   | |  :
%e A248890 :     :     :  o  :  o     o  :  o   o o     o   o o  :
%e A248890 :     :     :     :        |  :  |     |           |  :
%e A248890 :     :     :     :        o  :  o     o           o  :
%e A248890 :     :     :     :           :                    |  :
%e A248890 : n=1 : n=2 : n=3 :  n=4      :  n=5               o  :
%e A248890 :.....:.....:.....:...........:.......................:
%p A248890 g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A248890       binomial(g((i-1)$2)+j-1, j)*g(n-i*j, i-1), j=0..min(i, n/i))))
%p A248890     end:
%p A248890 a:= n-> g((n-1)$2):
%p A248890 seq(a(n), n=0..40);
%t A248890 g[n_, i_] := g[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[g[i-1, i-1]+j-1, j]*g[n-i*j, i-1], {j, 0, Min[i, n/i]}]]]; a[n_] := g[n-1, n-1]; Table[ a[n], {n, 0, 40}] (* _Jean-François Alcover_, Feb 28 2017, translated from Maple *)
%Y A248890 Cf. A000081, A032305, A045648, A213920.
%K A248890 nonn
%O A248890 0,5
%A A248890 _Alois P. Heinz_, Mar 05 2015