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Search: id:A144643
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| A144643 |
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Triangle read by rows: T(n,k) = number of partitions of [1..k] into n nonempty clumps of sizes 1, 2, 3 or 4 (n >= 0, 0 <= k <= 4n). |
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+0
7
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| 1, 0, 1, 1, 1, 1, 0, 0, 1, 3, 7, 15, 25, 35, 35, 0, 0, 0, 1, 6, 25, 90, 280, 770, 1855, 3675, 5775, 5775, 0, 0, 0, 0, 1, 10, 65, 350, 1645, 6930, 26425, 90475, 275275, 725725, 1576575, 2627625, 2627625, 0, 0, 0, 0, 0, 1, 15, 140, 1050, 6825, 39795
(list; graph; listen)
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OFFSET
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0,10
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LINKS
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David Applegate and N. J. A. Sloane, The Gift Exchange Problem (arXiv:0907.0513, 2009)
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FORMULA
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For recurrence see Maple code.
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EXAMPLE
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Triangle begins:
1,
0, 1, 1, 1, 1,
0, 0, 1, 3, 7, 15, 25, 35, 35,
0, 0, 0, 1, 6, 25, 90, 280, 770, 1855, 3675, 5775, 5775,
0, 0, 0, 0, 1, 10, 65, 350, 1645, 6930, 26425, 90475, 275275, 725725, 1576575, 2627625, 2627625
0, 0, 0, 0, 0, 1, 15, 140, 1050, 6825, 39795, 211750, 1033725, 4629625, 18918900, 69719650, 227727500, 640264625, 1474097625, 2546168625, 2546168625
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MAPLE
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T := proc(n, k) option remember;
if n = k then 1;
elif k < n then 0;
elif n < 1 then 0;
else T(n - 1, k - 1) + (k - 1)*T(n - 1, k - 2) + 1/2*(k - 1)*(k - 2)*T(n - 1, k - 3) + 1/6*(k - 1)*(k - 2)*(k - 3)*T(n - 1, k - 4);
end if;
end proc;
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CROSSREFS
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Row sums give A144508. See A144644 and A144645 for other versions.
Cf. A144299, A144385.
Sequence in context: A131753 A001213 A114221 this_sequence A034757 A078869 A011890
Adjacent sequences: A144640 A144641 A144642 this_sequence A144644 A144645 A144646
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KEYWORD
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nonn,tabf
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AUTHOR
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David Applegate and N. J. A. Sloane (njas(AT)research.att.com), Jan 25 2009
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