A064782 Number of partially labeled rooted trees with n nodes (6 of which are labeled).

7776, 117649, 1071904, 7601777, 46205469, 252620693, 1277843841, 6088987597, 27669884619, 120970585689, 512143134419, 2110092318654, 8493720340735, 33506301271642, 129860760881905, 495506657571553, 1864611086321279

Offset: 6

Author

Vladeta Jovovic, Oct 19 2001

Keywords

• nonn

References

• J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 134.

Crossrefs

Column k=6 of A008295.

Cf. A042977.

Formula

G.f.: A(x) = B(x)^6*(7776-14543*B(x) +11758*B(x)^2 -5126*B(x)^3 +1200*B(x)^4 -120*B(x)^5)/(1-B(x))^11, where B(x) is g.f. for rooted trees with n nodes, cf. A000081.