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A244406 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 10.

%I A244406 #9 Feb 09 2015 11:03:03
%S A244406 1,2,6,17,50,143,416,1199,3474,10049,29118,84370,244718,710081,
%T A244406 2061842,5989898,17411214,50634907,147327663,428858279,1248914115,
%U A244406 3638554143,10604615353,30918735919,90178253585,263104102071,767878267996,2241762411780,6546561427512
%N A244406 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 10.
%H A244406 Alois P. Heinz, <a href="/A244406/b244406.txt">Table of n, a(n) for n = 11..750</a>
%p A244406 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A244406       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244406        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A244406     end:
%p A244406 a:= n-> b(n-1$2, 10$2) -`if`(k=0, 0, b(n-1$2, 9$2)):
%p A244406 seq(a(n), n=11..40);
%t A244406 b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]* b[n - i*j, i - 1, t - j, k], {j, 0, Min[t, n/i]}]] // FullSimplify] ; a[n_] := b[n - 1, n - 1, 10, 10] - If[n == 0, 0, b[n - 1, n - 1, 9, 9]]; Table[a[n], {n, 11, 40}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)
%Y A244406 Column k=10 of A244372.
%K A244406 nonn
%O A244406 11,2
%A A244406 _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014