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A071211 Triangular array T(n,k) read by rows, giving number of labeled free trees such that the root is smaller than all its children, with respect to the number n of vertices and to the label k of the root. 0
1, 3, 1, 16, 8, 3, 125, 75, 40, 16, 1296, 864, 540, 300, 125, 16807, 12005, 8232, 5292, 3024, 1296, 262144, 196608, 143360, 100352, 65856, 38416, 16807, 4782969, 3720087, 2834352, 2099520, 1492992, 995328, 589824, 262144, 100000000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

C. Chauve, S. Dulucq and O. Guibert, Enumeration of some labeled trees, Proceedings of FPSAC/SFCA 2000 (Moscow), Springer, pp. 146-157.

LINKS

Table of n, a(n) for n=1..37.

FORMULA

T(n,k) = (n-k)*(n+1)^(n-k-1)*n^(k-1).

MAPLE

T:= (n, k)-> (n-k)*(n+1)^(n-k-1)*n^(k-1):

seq(seq(T(n, k), k=0..n-1), n=1..10);

PROG

(PARI) tabl(nn) = {for (n=1, nn, for (k=0, n-1, print1((n-k)*(n+1)^(n-k-1)*n^(k-1), ", "); ); print(); ); } \\ Michel Marcus, Jun 27 2013

CROSSREFS

Cf. A000312, A000272 (first column).

Sequence in context: A143018 A102012 A128249 * A222029 A038675 A264902

Adjacent sequences:  A071208 A071209 A071210 * A071212 A071213 A071214

KEYWORD

easy,nonn,tabl

AUTHOR

Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002

STATUS

approved

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Last modified February 21 10:49 EST 2019. Contains 320372 sequences. (Running on oeis4.)