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

6,1

References

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

Links

Table of n, a(n) for n=6..22.

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.

Crossrefs

Column k=6 of A008295.

Cf. A042977.

Sequence in context: A223509 A187355 A190465 * A016865 A223561 A016913

Adjacent sequences: A064779 A064780 A064781 * A064783 A064784 A064785

Keyword

nonn

Author

Vladeta Jovovic, Oct 19 2001

Status

approved