A097173 Total number of green nodes among tricolored labeled trees on n nodes.

0, 2, 0, 48, 120, 4560, 35700, 1048992, 15514128, 456726240, 10073339100, 323266492560, 9361060088952, 336767513038320, 11913610172869860, 482920107426039360, 19998225191360977440, 909512248720724321472

Offset: 1

Author

Ralf Stephan, Jul 30 2004

Keywords

• nonn

Links

• S. Coulomb and M. Bauer, On vertex covers, matchings and random trees

Crossrefs

Cf. A097170, A097171, A097172, A097174, A000272.

Programs

Mathematica

Rest[CoefficientList[Series[LambertW[-LambertW[-x]]^2, {x, 0, 20}], x] * Range[0, 20]!] (* Vaclav Kotesovec, Aug 26 2016 *)

Formula

E.g.f.: A(x) = T(-T(x))^2, with T(x)=Sum[k=1..inf, A000169(k)/k!*x^k].

a(n) = -2 * n^(n-1) * Sum[l=1..n, (-l/n)^l*(1/l-1)*C(n, l)].

a(n) ~ 2*LambertW(1)^2*n^(n-1)/(1+LambertW(1)). - Vaclav Kotesovec, Aug 26 2016