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%I #16 Feb 28 2016 09:56:12
%S 0,1,3,15,82,495,3144,20874,142766,1000083,7136463,51699614,379214625,
%T 2810720045,21018835670,158389275075,1201541422730,9168456492986,
%U 70324572634341,541910543713685,4193257236992896,32568879336517050,253822497160605899,1984276479881989537,15556238037968354214,122274773948426045945
%N Number of directed rooted trees on n nodes with forbidden limbs.
%H T. Lu, <a href="http://dx.doi.org/10.1016/0012-365X(95)00041-T">The enumeration of trees with and without given limbs</a>, Discr. Math., 154 (1996), 153-165, example 5.
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F G.f. (x-x^7-x^8+x^13)/[Product_{p>=1} (1-x^p)^(3*a(p)], in implicit form. - _R. J. Mathar_, Feb 26 2016
%t nmax = 30; b = ConstantArray[0, nmax+1]; b[[1]] = 0; b[[2]] = 1; Do[b[[n+1]] = SeriesCoefficient[(x-x^7-x^8+x^13) / Product[(1 - x^p)^(3*b[[p+1]]), {p, 1, n-1}], {x, 0, n}], {n, 2, nmax}]; b (* _Vaclav Kotesovec_, Feb 28 2016 *)
%Y Cf. A006964.
%K nonn
%O 0,3
%A _N. J. A. Sloane_.
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