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%I #15 Feb 06 2015 08:10:41
%S 1,0,1,2,4,7,15,28,56,110,220,436,878,1762,3560,7205,14650,29838,
%T 60991,124938,256628,528238,1089834,2252860,4666304,9682422,20125777,
%U 41900433,87369029,182441944,381499040,798782945,1674575394,3514733683,7385298837,15534856067
%N Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 2.
%H Alois P. Heinz, <a href="/A244456/b244456.txt">Table of n, a(n) for n = 3..900</a>
%F a(n) ~ c * d^n / n^(3/2), where d = A246403 = 2.18946198566085056388702757711..., c = 0.4213018528699249210965028... (constants are same as for A001679). - _Vaclav Kotesovec_, Jul 02 2014
%e a(5) = 1:
%e o
%e / \
%e o o
%e / \
%e o o
%p b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k],
%p 1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p b(n-i*j, i-1, max(0,t-j), k), j=0..n/i)))
%p end:
%p a:= n-> b(n-1$2, 2$2) -b(n-1$2, 3$2):
%p seq(a(n), n=3..40);
%t b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]*b[n - i*j, i - 1, Max[0, t - j], k], {j, 0, n/i}]]]; a[n_] := b[n - 1, n - 1, 2, 2] - b[n - 1, n - 1, 3, 3] // FullSimplify; Table[a[n], {n, 3, 40}] (* _Jean-François Alcover_, Feb 06 2015, after Maple *)
%Y Column k=2 of A244454.
%Y Cf. A244531, A246403.
%K nonn
%O 3,4
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 29 2014
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