A014265 - OEIS

%I #14 Feb 27 2016 17:56:35

%S 0,1,1,1,2,2,4,7,15,30,68,146,340,786,1878,4507,11045,27220,67956,

%T 170766,432818,1103539,2831814,7303966,18934866,49302321,128910528,

%U 338329555,891099316,2354613762,6240696052,16587146598,44203851675,118093003229

%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.

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F G.f. x^5 + t(x)-(t(x)^2-t(x^2))/2, where t(x) = (x-2*x^5+x^9)/[Product_{p>=1} (1-x^p)^b(p)] is the implicit form of the ordinary generating function of the sequence b(n>=0) = 0,1, 1, 2, 4, 7, 16, 38, 89, 217, 535, 1340, 3391, 8686, 22421, 58355, 152859,... - _R. J. Mathar_, Feb 27 2016

%K nonn

%O 0,5

%A _N. J. A. Sloane_.