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A014278 Number of trees on n nodes with 3 forbidden limbs of size 4, 5 and 6. 1

%I

%S 0,1,1,2,3,6,12,30,67,159,381,929,2282,5680,14241,36009,91611,234512,

%T 603330,1559582,4047956,10546556,27570983,72301171,190136444,

%U 501323021,1324981299,3509660618,9315633928,24773632117,65999430834,176121938800,470720836811,1259936118810,3376997883966,9063076063854

%N Number of trees on n nodes with 3 forbidden limbs of size 4, 5 and 6.

%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 6.

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

%F G.f. (x-x^4-x^5-x^6+2*x^7)/[Product_{p>=1} (1-x^p)^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-x^4-x^5-x^6+2*x^7) / Product[(1 - x^p)^(b[[p+1]]), {p, 1, n-1}], {x, 0, n}], {n, 2, nmax}]; b (* _Vaclav Kotesovec_, Feb 28 2016 *)

%K nonn

%O 0,4

%A _N. J. A. Sloane_.

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Last modified November 18 17:33 EST 2019. Contains 329287 sequences. (Running on oeis4.)