A014273 - OEIS

%I #17 Feb 28 2016 09:39:44

%S 0,1,2,5,19,73,297,1256,5467,24368,110610,509715,2377978,11210451,

%T 53318599,255537199,1232866889,5982965779,29185293329,143026402189,

%U 703829126231,3476496240860,17230140895115,85659915381510,427065111704502,2134705956413458

%N Number of trees on n nodes with forbidden limbs.

%H Vaclav Kotesovec, <a href="/A014273/b014273.txt">Table of n, a(n) for n = 0..1000</a>

%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^4)/[Product_{p >= 1} (1-x^p)^(2*a(p))], in implicit form. - _R. J. Mathar_, Feb 26 2016

%F a(n) ~ c * d^n / n^(3/2), where d = 5.31351404806511900111976949727598017431010423107784202438023676025442... and c = 0.19638268380963259854038594083610578852611575... . - _Vaclav Kotesovec_, Feb 28 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^4) / 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_.