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%I #14 Feb 03 2018 17:03:39
%S 1,2,6,17,50,143,416,1199,3474,10049,29119,84377,244748,710199,
%T 2062274,5991418,17416401,50652248,147384676,429043390,1249508947,
%U 3640449679,10610613552,30937605076,90237313083,263288153074,768449666117,2243530461067,6552016136667
%N Number of unlabeled rooted trees with 2n nodes and maximal outdegree (branching factor) n.
%H Alois P. Heinz, <a href="/A244407/b244407.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = A244372(2n,n).
%F a(n) ~ c * d^n / sqrt(n), where d = 2.955765285651994974714817524... is the Otter's rooted tree constant (see A051491), and c = 0.9495793... . - _Vaclav Kotesovec_, Jul 11 2014
%p b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p end:
%p a:= n-> b(2*n-1$2, n$2)-b(2*n-1$2, n-1$2):
%p seq(a(n), n=1..30);
%t 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[2*n - 1, 2 n - 1, n, n] - b[2*n - 1, 2 n - 1, n - 1, n - 1]; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Feb 06 2015, after Maple *)
%Y Cf. A244372, A244410, A051491, A299039.
%K nonn
%O 1,2
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014
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