|
Search: id:A135814
|
|
|
| A135814 |
|
Triangle of numbers of coincidence-free length n-m lists of m-tuples with all numbers 1,...,n-m in tuple position k, for k=1..m. . |
|
+0
3
|
|
| 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 2, 3, 0, 1, 0, 9, 26, 7, 0, 1, 0, 44, 453, 194, 15, 0, 1, 0, 265, 11844, 13005, 1250, 31, 0, 1, 0, 1854, 439975, 1660964, 326685, 7682, 63, 0, 1, 0, 14833, 22056222, 363083155, 205713924, 7931709, 46466, 127, 0, 1, 0, 133496
(list; table; graph; listen)
|
|
|
OFFSET
|
0,12
|
|
|
COMMENT
|
a(n,m), n>=m, enumerates (ordered) length n-m lists of m-tuples such that every number from 1 to n-m appears once at each of the n-m tuple positions, and the j-th list member is not the tuple (j,j,...,j) (m times j), for every j=1,..,n. Called coincidence-free m-tuple lists of length n-m. See the Charalambides reference for this combinatorial interpretation.
The column sequences (without leading zeros) give A000007, A000166 (subfactorials), A089041, A135809 - A135813, for m=0..7.
|
|
REFERENCES
|
Ch. A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, p. 187, Exercise 13.(a).
|
|
LINKS
|
W. Lang, First 10 rows and more.
|
|
FORMULA
|
a(n,m)= sum(((-1)^(n-m-j))*binomial(n-m,j)*(j!)^m,j=0..n-m), n >= m >= 0, else 0.
|
|
EXAMPLE
|
[1];[0,1];[0,0,1];[0,1,0,1];[,0,2,3,0,1];[0,9,26,7,0,1],...
|
|
CROSSREFS
|
Sequence in context: A054439 A064722 A123735 this_sequence A038570 A103498 A030386
Adjacent sequences: A135811 A135812 A135813 this_sequence A135815 A135816 A135817
|
|
KEYWORD
|
nonn,easy,tabl
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jan 21 2008, Feb 22 2008
|
|
|
Search completed in 0.002 seconds
|
