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A014267 Number of rooted trees on n nodes with forbidden limbs. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A318799

Adjacent sequences:  A014264 A014265 A014266 * A014268 A014269 A014270

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 24 18:12 EDT 2019. Contains 326295 sequences. (Running on oeis4.)