A097628 Number of rooted directed trees on n nodes with a green root.

0, 2, 15, 232, 4535, 114276, 3478083, 124625040, 5135162607, 239298611020, 12443586907763, 714352426078776, 44874695909075799, 3061971330141166548, 225519631138748009955, 17832309102333780001312

Offset: 1

Author

Ralf Stephan, Aug 17 2004

Keywords

• nonn

Comments

Ditrees are well-colored directed trees. Well-colored means, each green vertex has at least a red child, each red vertex has no red child.

Links

• C. Banderier, J.-M. Le Bars and V. Ravelomanana, Generating functions for kernels of digraphs, arXiv:math/0411138 [math.CO], 2004.

Crossrefs

Equals A052746(n) - A097627(n).

Programs

Mathematica

terms = 16;
c[x_] = -LambertW[-x];
A[x_] = c[2x]/2 + c[-c[2x]/2];
CoefficientList[A[x]/x + O[x]^terms, x] Range[terms]! (* Jean-François Alcover, Jan 15 2019 *)

Formula

E.g.f.: A(x) = C(2x)/2+C(-C(2x)/2), C(x) = e.g.f. of A000169.