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A365330
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Expansion of e.g.f. x^3/(1-x-x^2-x^3)^2.
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0
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0, 0, 0, 6, 48, 600, 8640, 131040, 2257920, 42819840, 885427200, 19918483200, 483791616000, 12622171161600, 352200296448000, 10466625641472000, 330077933273088000, 11010660024139776000, 387369218691366912000, 14335266857678807040000, 556691771706962411520000
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OFFSET
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0,4
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COMMENTS
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a(n) is the number of ways to partition [n] into blocks of size at most 3, order the blocks, order the elements within each block, and choose 3 elements from a block.
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LINKS
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FORMULA
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EXAMPLE
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a(6)=8640 since the ways to partition [6] into blocks of size at most 3, order the blocks, order the elements within each block, and select 3 elements from a block are the following:
(i) 123,4,5,6: 2880 such orderings, 1 way to choose three elements (from the block with 3 elements), hence 2880 ways;
(ii) 123,45,6: 4320 such orderings, 1 way to choose three elements (from the block with 3 elements), hence 4320 ways;
(iii) 123,456: 720 such orderings, 2 ways to choose three elements (from one of the two blocks with 3 elements), hence 1440 ways.
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MATHEMATICA
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With[{m = 20}, Range[0, m]! * CoefficientList[Series[x^3/(1 - x - x^2 - x^3)^2, {x, 0, m}], x]] (* Amiram Eldar, Sep 02 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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