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A145460
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Square array A(n,k), n>=0, k>=0, read by antidiagonals, where sequence a_k of column k is the exponential transform of C(n,k).
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7
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1, 1, 1, 1, 1, 2, 1, 0, 3, 5, 1, 0, 1, 10, 15, 1, 0, 0, 3, 41, 52, 1, 0, 0, 1, 9, 196, 203, 1, 0, 0, 0, 4, 40, 1057, 877, 1, 0, 0, 0, 1, 10, 210, 6322, 4140, 1, 0, 0, 0, 0, 5, 30, 1176, 41393, 21147, 1, 0, 0, 0, 0, 1, 15, 175, 7273, 293608, 115975, 1, 0, 0, 0, 0, 0, 6, 35, 1176
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| A(n,k) is also the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box k balls are seen at the top. E.g. A(3,1)=10:
|1.| |2.| |3.| |1|2| |1|2| |1|3| |1|3| |2|3| |2|3| |1|2|3|
|23| |13| |12| |3|.| |.|3| |2|.| |.|2| |1|.| |.|1| |.|.|.|
+--+ +--+ +--+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+-+
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..10010
N. J. A. Sloane, Transforms
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EXAMPLE
| Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 0, 0, 0, 0, ...
2, 3, 1, 0, 0, 0, ...
5, 10, 3, 1, 0, 0, ...
15, 41, 9, 4, 1, 0, ...
52, 196, 40, 10, 5, 1, ...
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MAPLE
| exptr:= proc(p) local g; g:= proc(n) option remember; local j; `if` (n=0, 1, add (binomial (n-1, j-1) *p(j) *g(n-j), j=1..n)) end: end: A:= (n, k)-> exptr (i-> binomial (i, k)) (n): seq (seq (A(n, d-n), n=0..d), d=0..12);
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CROSSREFS
| Columns 0-9 give: A000110, A000248, A133189 A145453, A145454, A145455, A145456, A145457, A145458, A145459. Cf.: A007318, A143398.
Sequence in context: A135488 A099493 A088523 * A202178 A035543 A105546
Adjacent sequences: A145457 A145458 A145459 * A145461 A145462 A145463
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KEYWORD
| nonn,tabl
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 10 2008
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