%I #15 Feb 28 2016 09:47:48
%S 0,1,2,5,18,70,282,1189,5144,22804,102908,471477,2186648,10247609,
%T 48449798,230819691,1106961890,5339801036,25891658674,126123321469,
%U 616916700222,3028854625890,14921089624916,73733085073247,365384562116904,1815365194118833
%N Number of 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 4.
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F G.f. (x-2*x^3+x^5)/[Product_{p>=1} (1-x^p)^(2*a(p))], implicit form. - _R. J. Mathar_, Feb 27 2016
%t nmax = 30; b = ConstantArray[0, nmax+1]; b[[1]] = 0; b[[2]] = 1; Do[b[[n+1]] = SeriesCoefficient[(x-2*x^3+x^5) / Product[(1 - x^p)^(2*b[[p+1]]), {p, 1, n-1}], {x, 0, n}], {n, 2, nmax}]; b (* _Vaclav Kotesovec_, Feb 28 2016 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_.
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