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A131103
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Rectangular array read by antidiagonals: a(n, k) is the number of ways to put k labeled objects into n labeled boxes so that there are no boxes with exactly one object (n, k >= 1).
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3
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0, 0, 1, 0, 2, 1, 0, 3, 2, 1, 0, 4, 3, 8, 1, 0, 5, 4, 21, 22, 1, 0, 6, 5, 40, 63, 52, 1, 0, 7, 6, 65, 124, 243, 114, 1, 0, 8, 7, 96, 205, 664, 969, 240, 1, 0, 9, 8, 133, 306, 1405, 3196, 3657, 494, 1, 0, 10, 9, 176, 427, 2556, 7425, 15712, 12987, 1004, 1, 0, 11, 10, 225, 568, 4207
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Problem suggested by Brandon Zeidler. Columns four and five are A000567 and A051874. Second row is A130102.
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FORMULA
| a(n, k) = sum_{j=1..min(floor(k/2), n)} A008299(k, j)*n!/(n-j)!.
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EXAMPLE
| Array begins:
0 1 1 1 1 1 1
0 2 2 8 22 52 114
0 3 3 21 63 243 969
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CROSSREFS
| Cf. A131104, A131105, A131106, A131107.
Sequence in context: A025663 A025647 A025653 * A180653 A096652 A025654
Adjacent sequences: A131100 A131101 A131102 * A131104 A131105 A131106
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| David Wasserman (dwasserm(AT)earthlink.net), Jun 14 2007, Jun 15 2007
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