A014267 Number of rooted trees on n nodes with forbidden limbs.

0, 1, 1, 2, 4, 9, 20, 47, 112, 279, 701, 1794, 4636, 12130, 31987, 85062, 227673, 613126, 1659712, 4514249, 12329670, 33804673, 93001852, 256667215, 710381240, 1971312184, 5483656721, 15288227949, 42711458197, 119555284629, 335253287132

Offset

0,4

Links

Table of n, a(n) for n=0..30.

T. Lu, The enumeration of trees with and without given limbs, Discr. Math., 154 (1996), 153-165, Example 3.

Index entries for sequences related to rooted trees

Formula

G.f. (x-x^7-x^8+x^13)/[Product_{p>=1} (1-x^p)^a(p)], 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)^b[[p+1]], {p, 1, n-1}], {x, 0, n}], {n, 2, nmax}]; b (* Vaclav Kotesovec, Feb 28 2016 *)

Crossrefs

Sequence in context: A036619 A036620 A036721 * A089405 A091500 A370718

Adjacent sequences: A014264 A014265 A014266 * A014268 A014269 A014270

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved