|
Search: id:A081718
|
|
|
| A081718 |
|
Array T(m,n) read by antidiagonals, where T(m,n) = number of m X infinity multiplicity integer partition (mip) matrix of n (m >= 0, n >= 0). |
|
+0
2
|
|
| 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 3, 3, 1, 0, 1, 1, 4, 6, 5, 1, 0, 1, 1, 5, 10, 13, 7, 1, 0, 1, 1, 6, 15, 26, 23, 11, 1, 0, 1, 1, 7, 21, 45, 55, 44, 15, 1, 0, 1, 1, 8, 28, 71, 110, 121, 74, 22, 1, 0, 1, 1, 9, 36, 105, 196, 271, 237, 129, 30, 1, 0, 1, 1, 10, 45, 148, 322, 532
(list; table; graph; listen)
|
|
|
OFFSET
|
0,13
|
|
|
COMMENT
|
For n > 0, the n-th column is given by a polynomial of degree n-1. - David Wasserman (wasserma(AT)spawar.navy.mil), Jun 21 2004
|
|
REFERENCES
|
W. C. Yang, Derivatives are essentially integer partitions, Discrete Math., 222 (2000), 235-245.
|
|
FORMULA
|
There is a recurrence involving the partition function.
|
|
EXAMPLE
|
Array begins:
1 1 0 0 0 ...
1 1 1 1 1 ...
1 1 2 3 5 ...
1 1 3 6 13 ...
|
|
CROSSREFS
|
Rows and columns give A022811, A022812, A022813, A022814, A022815, etc.
Sequence in context: A133607 A103631 A083856 this_sequence A129634 A066438 A051126
Adjacent sequences: A081715 A081716 A081717 this_sequence A081719 A081720 A081721
|
|
KEYWORD
|
nonn,tabl,easy
|
|
AUTHOR
|
njas, Apr 05 2003
|
|
EXTENSIONS
|
More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jun 21 2004
|
|
|
Search completed in 0.002 seconds
|
