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A244399 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 3.

%I A244399 #13 Aug 15 2015 12:02:46
%S A244399 1,2,6,16,43,113,300,787,2074,5460,14391,37960,100275,265187,702307,
%T A244399 1862463,4945952,13152441,35023003,93385548,249330208,666539949,
%U A244399 1784102735,4781254117,12828545419,34459732110,92668129050,249469906115,672296028786,1813606782459
%N A244399 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 3.
%H A244399 Alois P. Heinz, <a href="/A244399/b244399.txt">Table of n, a(n) for n = 4..1000</a>
%F A244399 a(n) = A000598(n) - A001190(n+1) = A000598(n) - A036656(n+1).
%F A244399 a(n) ~ c * d^n / n^(3/2), where d = 1/A261340 = 2.81546003317615... and c = 0.5178759064... . - _Vaclav Kotesovec_, Jun 27 2014
%p A244399 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A244399       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244399        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A244399     end:
%p A244399 a:= n-> b(n-1$2, 3$2) -`if`(k=0, 0, b(n-1$2, 2$2)):
%p A244399 seq(a(n), n=4..35);
%t A244399 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, 3, 3] - If[n == 0, 0, b[n-1, n-1, 2, 2]]; Table[a[n], {n, 4, 35}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)
%Y A244399 Column k=3 of A244372.
%Y A244399 Cf. A000598, A001190, A036656.
%K A244399 nonn
%O A244399 4,2
%A A244399 _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014