A014271 Number of trees on n nodes with forbidden limbs.

0, 1, 2, 5, 18, 70, 282, 1189, 5144, 22804, 102908, 471477, 2186648, 10247609, 48449798, 230819691, 1106961890, 5339801036, 25891658674, 126123321469, 616916700222, 3028854625890, 14921089624916, 73733085073247, 365384562116904, 1815365194118833

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 4.

Index entries for sequences related to trees

Formula

G.f. (x-2*x^3+x^5)/[Product_{p>=1} (1-x^p)^(2*a(p))], implicit form. - R. J. Mathar, Feb 27 2016

Mathematica

nmax = 30; b = ConstantArray[0, nmax+1]; b[[1]] = 0; b[[2]] = 1; Do[b[[n+1]] = SeriesCoefficient[(x-2*x^3+x^5) / Product[(1 - x^p)^(2*b[[p+1]]), {p, 1, n-1}], {x, 0, n}], {n, 2, nmax}]; b (* Vaclav Kotesovec, Feb 28 2016 *)

Crossrefs

Sequence in context: A322555 A118814 A345878 * A073157 A365120 A268570

Adjacent sequences: A014268 A014269 A014270 * A014272 A014273 A014274

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved