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Search: id:A145460
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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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+0
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; listen)
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OFFSET
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0,6
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COMMENT
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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
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N. J. A. Sloane, Transforms
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EXAMPLE
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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
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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
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Columns 0-9 give: A000110, A000248, A133189 A145453, A145454, A145455, A145456, A145457, A145458, A145459. Cf.: A007318, A143398.
Sequence in context: A135488 A099493 A088523 this_sequence A035543 A105546 A059297
Adjacent sequences: A145457 A145458 A145459 this_sequence A145461 A145462 A145463
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 10 2008
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