A248890 - OEIS

%I #10 Feb 28 2017 12:08:20

%S 0,1,1,1,2,4,8,16,34,75,166,374,849,1952,4522,10566,24840,58760,

%T 139693,333702,800412,1927207,4655997,11283835,27423930,66825194,

%U 163227234,399587270,980222058,2409181633,5931839530,14629639579,36137308192,89395224033

%N 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 Alois P. Heinz, <a href="/A248890/b248890.txt">Table of n, a(n) for n = 0..1000</a>

%e :  o  :  o  :  o  :    o   o  :    o     o     o   o  :

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%e :     :  o  :  o  :  o   o o  :    o   o   o o   o o  :

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%e :     :     :  o  :  o     o  :  o   o o     o   o o  :

%e :     :     :     :        |  :  |     |           |  :

%e :     :     :     :        o  :  o     o           o  :

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%e : n=1 : n=2 : n=3 :  n=4      :  n=5               o  :

%e :.....:.....:.....:...........:.......................:

%p g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(

%p       binomial(g((i-1)$2)+j-1, j)*g(n-i*j, i-1), j=0..min(i, n/i))))

%p     end:

%p a:= n-> g((n-1)$2):

%p seq(a(n), n=0..40);

%t 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 Cf. A000081, A032305, A045648, A213920.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Mar 05 2015