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A064785 Partially labeled trees with n nodes (6 of which are labeled). 1
1296, 16807, 134960, 858578, 4741835, 23786827, 111254536, 493289047, 2096891419, 8614217489, 34402073301, 134162057607, 512703873915, 1925300176534, 7120276125066, 25981116938906, 93678940211218 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

REFERENCES

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 138.

LINKS

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

FORMULA

G.f.: A(x) = B(x)^6*(1296-2633*B(x)+2128*B(x)^2-806*B(x)^3+120*B(x)^4)/(1-B(x))^9, where B(x) is g.f. for rooted trees with n nodes, cf. A000081.

MAPLE

b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember; add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember; add(b(k)*x^k, k=1..n) end: a:= n-> coeff(series(B(n-2)^6* (1296-2633* B(n-2)+ 2128*B(n-2)^2 -806*B(n-2)^3 +120*B(n-2)^4)/ (1-B(n-2))^9, x=0, n+1), x, n): seq(a(n), n=6..22); # Alois P. Heinz, Aug 22 2008

CROSSREFS

Cf. A000055, A000081, A000243, A000269, A000485, A000526, A000107, A000524, A000444, A000525, A042977.

Sequence in context: A250438 A221006 A016864 * A223560 A016912 A330980

Adjacent sequences:  A064782 A064783 A064784 * A064786 A064787 A064788

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Oct 19 2001

STATUS

approved

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Last modified May 31 07:30 EDT 2020. Contains 334747 sequences. (Running on oeis4.)