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%I #17 Sep 08 2022 08:45:32
%S 2,16,288,8192,320000,15925248,963780608,68719476736,5642219814912,
%T 524288000000000,54394721876836352,6232805962420322304,
%U 781754012972500385792,106530593546206374264832,15672832819200000000000000,2475880078570760549798248448
%N Number of labeled marked rooted trees with n nodes.
%C A marked rooted tree is a rooted tree where each node and edge is marked as + or -.
%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 293 (4.1.60).
%H Vincenzo Librandi, <a href="/A136796/b136796.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F E.g.f.: B(4*x)/2 where B(x) is e.g.f. of A000169.
%F a(n) = A052764(n)*2.
%F a(n) = 2^(2*n-1) * n^(n-1). - _Vaclav Kotesovec_, Mar 29 2014
%t Table[2^(2*n-1)*n^(n-1),{n,1,20}] (* _Vaclav Kotesovec_, Mar 29 2014 *)
%o (Magma) [2^(2*n-1)*n^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Mar 29 2014
%Y Cf. A136794 (unlabeled version), A136797 (tree version).
%K nonn
%O 1,1
%A _Christian G. Bower_, Jan 21 2008
%E More terms from _Vincenzo Librandi_, Mar 29 2014
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