A365330 Expansion of e.g.f. x^3/(1-x-x^2-x^3)^2.
0, 0, 0, 6, 48, 600, 8640, 131040, 2257920, 42819840, 885427200, 19918483200, 483791616000, 12622171161600, 352200296448000, 10466625641472000, 330077933273088000, 11010660024139776000, 387369218691366912000, 14335266857678807040000, 556691771706962411520000
Offset: 0
Keywords
Examples
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.
Programs
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Mathematica
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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