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A285795
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Sum of the second entries in all cycles of all permutations of [n].
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2
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0, 0, 2, 13, 83, 582, 4554, 39672, 382248, 4044240, 46663920, 583554240, 7865622720, 113711230080, 1755484617600, 28828769356800, 501858148377600, 9232213174732800, 178968924600883200, 3646603415927808000, 77916767838981120000, 1742147265551616000000
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OFFSET
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0,3
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COMMENTS
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Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
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LINKS
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EXAMPLE
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a(3) = 13 because the sum of the second entries in all cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 2+3+2+3+3+0 = 13.
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MAPLE
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a:= proc(n) option remember; `if`(n<3, n*(n-1),
((2*n^2+3*n-1)*a(n-1)-(n-1)*n*(n+2)*a(n-2))/(n+1))
end:
seq(a(n), n=0..25);
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MATHEMATICA
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Flatten[{0, Table[n! * (2*(n+1)*HarmonicNumber[n] - n - 3)/4, {n, 1, 25}]}] (* Vaclav Kotesovec, Apr 29 2017 *)
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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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