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A306258
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a(n) = floor(n^2/4)*n!.
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2
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0, 0, 2, 12, 96, 720, 6480, 60480, 645120, 7257600, 90720000, 1197504000, 17244057600, 261534873600, 4271736268800, 73229764608000, 1339058552832000, 25609494822912000, 518592270163968000, 10948059036794880000, 243290200817664000000
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OFFSET
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0,3
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COMMENTS
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a(n) is the total displacement of all letters in all permutations on n letters as if the first letter were connected to the last letter, forming a loop.
For the sequence A090672 the displacement of the permutation "0123" is 0, while that of the permutation "3210" is 8 because each of the digits 0 and 3 is 3 places away from its original place and each of the digits 1 and 2 is one place away, so the total displacement is 3+1+1+3 = 8.
In this sequence, however, the displacement is calculated differently: that of "0123" is 0 as before, but the displacement of "3210" is no longer 8 because the first index and last index are connected, forming a loop; each of the digits 0 and 3 is now 1 place away from its original place (and each of the digits 1 and 2 is one place away, as before), so the total displacement is calculated as 1+1+1+1 = 4.
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LINKS
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FORMULA
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a(n) = floor(n^2/4)*n!.
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MATHEMATICA
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PROG
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(PARI) a(n) = floor(n^2/4)*n!;
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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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