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A244405 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 9.

%I A244405 #8 Feb 09 2015 11:03:10
%S A244405 1,2,6,17,50,143,416,1199,3474,10048,29112,84347,244630,709767,
%T A244405 2060754,5986231,17399060,50595235,147199567,428448576,1247613511,
%U A244405 3634451971,10591746511,30878554201,90053295475,262716880036,766682072349,2238077375703,6535237181868
%N A244405 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 9.
%H A244405 Alois P. Heinz, <a href="/A244405/b244405.txt">Table of n, a(n) for n = 10..750</a>
%p A244405 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A244405       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244405        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A244405     end:
%p A244405 a:= n-> b(n-1$2, 9$2) -`if`(k=0, 0, b(n-1$2, 8$2)):
%p A244405 seq(a(n), n=10..45);
%t A244405 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, 9, 9] - If[n == 0, 0, b[n - 1, n - 1, 8, 8]]; Table[a[n], {n, 10, 45}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)
%Y A244405 Column k=9 of A244372.
%K A244405 nonn
%O A244405 10,2
%A A244405 _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014