The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A071209

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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 size k of the subtree rooted at the vertex labeled by 1.
(history; published version)

#9 by Joerg Arndt at Fri Jun 28 01:24:58 EDT 2013

STATUS

reviewed

approved

#8 by Charles R Greathouse IV at Thu Jun 27 10:22:10 EDT 2013

STATUS

proposed

reviewed

Discussion

Thu Jun 27

10:26

Michel Marcus: Or you could have :
http://link.springer.com/chapter/10.1007%2F978-3-662-04166-6_13.

But since I did not get same data, I thought it might help to see paper even a .ps file.

#7 by Michel Marcus at Thu Jun 27 03:24:29 EDT 2013

STATUS

editing

proposed

Discussion

Thu Jun 27

10:18

Charles R Greathouse IV: If the only link we have is postscript, I support that. I'd rather see a direct link than one to the general publication page.

#6 by Michel Marcus at Thu Jun 27 03:22:59 EDT 2013

LINKS

C. Chauve, S. Dulucq and O. Guibert, <a href="http://www.cecm.sfu.ca/~cchauve/Publications/SFCA00.ps">Enumeration of some labeled trees</a>

Discussion

Thu Jun 27

03:24

Michel Marcus: Postscript link , is this OK ?
Or pointer to http://www.cecm.sfu.ca/~cchauve/publications.html

#5 by Michel Marcus at Thu Jun 27 03:07:45 EDT 2013

OFFSET

2,1,5

PROG

(PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(binomial(n, k-1)*k^(k-2)*(n-k)^(n+1-k), ", "); ); print(); ); } \\ Michel Marcus, Jun 27 2013

STATUS

approved

editing

Discussion

Thu Jun 27

03:13

Michel Marcus: Problem : I get something quite different:
0,
1, 0,
8, 3, 0,
81, 32, 18, 0,

whereas current data have 
0  
1  1  
0  3  8  
3  0  16  81

#4 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

binomial(n, k-1)*k^(k-2)*(n-k)^(n+1-k)

KEYWORD

easy,nonn,tabl,new

#3 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

REFERENCES

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

KEYWORD

easy,nonn,tabl,new

#2 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

REFERENCES

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

KEYWORD

easy,nonn,tabl,new

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

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 size k of the subtree rooted at the vertex labeled by 1.

DATA

0, 1, 1, 0, 3, 8, 3, 0, 16, 81, 32, 18, 0, 125, 1024, 405, 240, 160, 0, 1296, 15625, 6144, 3645, 2560, 1875, 0, 16807, 279936, 109375, 64512, 45360, 35000, 27216, 0, 262144, 5764801, 2239488, 1312500, 917504, 708750, 580608, 470596, 0, 4782969

OFFSET

2,5

REFERENCES

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

FORMULA

binomial(n,k-1)*k^(k-2)*(n-k)^(n+1-k)

MAPLE

(n, k) -> binomial(n, k-1)*k^(k-2)*(n-k)^(n+1-k);

CROSSREFS

Cf. A000312.

KEYWORD

easy,nonn,tabl

AUTHOR

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

STATUS

approved