A014276 Number of directed rooted trees on n nodes with forbidden limbs.

0, 1, 3, 15, 82, 495, 3144, 20874, 142766, 1000083, 7136463, 51699614, 379214625, 2810720045, 21018835670, 158389275075, 1201541422730, 9168456492986, 70324572634341, 541910543713685, 4193257236992896, 32568879336517050, 253822497160605899, 1984276479881989537, 15556238037968354214, 122274773948426045945

Offset

0,3

Links

Table of n, a(n) for n=0..25.

T. Lu, The enumeration of trees with and without given limbs, Discr. Math., 154 (1996), 153-165, example 5.

Index entries for sequences related to rooted trees

Formula

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

Mathematica

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 *)

Crossrefs

Cf. A006964.

Sequence in context: A084208 A059271 A345885 * A006964 A371616 A203507

Adjacent sequences: A014273 A014274 A014275 * A014277 A014278 A014279

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved