A064781 Number of partially labeled rooted trees with n nodes (5 of which are labeled).

625, 7776, 60387, 373895, 2019348, 9941905, 45765687, 200160586, 840783867, 3418136039, 13525307849, 52314181361, 198451152867, 740283848220, 2721325964209, 9875523648986, 35429691205221, 125814678386528

Offset: 5

Author

Vladeta Jovovic, Oct 19 2001

Keywords

• nonn

References

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

Crossrefs

Column k=5 of A008295.

Cf. A042977.

Formula

G.f.: A(x) = B(x)^5*(625-974*B(x)+622*B(x)^2-192*B(x)^3+24*B(x)^4)/(1-B(x))^9, where B(x) is g.f. for rooted trees with n nodes, cf. A000081.