A064781 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

5,1

REFERENCES

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

LINKS

Table of n, a(n) for n=5..22.

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.

CROSSREFS

Column k=5 of A008295.

Cf. A042977.

Sequence in context: A046756 A143026 A238700 * A372845 A250832 A250827

Adjacent sequences: A064778 A064779 A064780 * A064782 A064783 A064784

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Oct 19 2001

STATUS

approved