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A144512
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Array read by upwards antidiagonals: T(n,k) = total number of partitions of [1, 2, ..., k] into exactly n blocks, each of size 1, 2, ..., k+1, for 0 <= k <= (k+1)*n.
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4
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1, 1, 1, 1, 2, 1, 1, 3, 7, 1, 1, 4, 31, 37, 1, 1, 5, 121, 842, 266, 1, 1, 6, 456, 18252, 45296, 2431, 1, 1, 7, 1709, 405408, 7958726, 4061871, 27007, 1, 1, 8, 6427, 9268549, 1495388159, 7528988476, 546809243, 353522, 1, 1, 9, 24301, 216864652, 295887993624, 15467641899285
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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LINKS
| David Applegate and N. J. A. Sloane, The Gift Exchange Problem (arXiv:0907.0513, 2009)
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EXAMPLE
| Array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 7, 37, 266, 2431, 27007, 353522, 5329837, ...
1, 3, 31, 842, 45296, 4061871, 546809243, 103123135501, ...
1, 4, 121, 18252, 7958726, 7528988476, 13130817809439, ...
1, 5, 456, 405408, 1495388159, 15467641899285, 361207016885536095, ...
1, 6, 1709, 9268549, 295887993624, 34155922905682979, 10893033763705794846727, ...
...
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MAPLE
| b := proc(n, i, k) local r;
option remember;
if n = i then 1;
elif i < n then 0;
elif n < 1 then 0;
else add( binomial(i-1, r)*b(n-1, i-1-r, k), r=0..k);
end if;
end proc;
T:=proc(n, k); add(b(n, i, k), i=0..(k+1)*n); end proc;
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CROSSREFS
| See A144510 for Maple code.
Rows include A001515, A144416, A144508, A144509, A149187.
Columns include A048775, A144511, A144662, A147984.
Transpose of array in A144510.
Sequence in context: A163181 A074662 A025243 * A159314 A135701 A051467
Adjacent sequences: A144509 A144510 A144511 * A144513 A144514 A144515
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KEYWORD
| nonn,tabl
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AUTHOR
| David Applegate and N. J. A. Sloane (njas(AT)research.att.com), Dec 15 2008, Dec 21 2008
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