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A285232
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Number of entries in the fourth cycles of all permutations of [n].
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2
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1, 12, 119, 1177, 12217, 135302, 1606446, 20450052, 278604252, 4051377504, 62702222112, 1029832270848, 17899305402240, 328353314855040, 6341705227082880, 128655706986282240, 2735782096305749760, 60855815849067648000, 1413487524282196608000
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OFFSET
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4,2
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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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FORMULA
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MAPLE
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a:= proc(n) option remember; `if`(n<5, [0$4, 1][n+1],
((n-2)*(3*n^2-13*n+6)*a(n-1)-(3*n^4-26*n^3+76*n^2
-81*n+16)*a(n-2)+(n-3)^4*n*a(n-3))/((n-1)*(n-4)))
end:
seq(a(n), n=4..30);
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MATHEMATICA
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a[3]=0; a[4]=1; a[5]=12; a[n_] := a[n] = ((n-2)(3n^2 - 13n + 6) a[n-1] - ( 3n^4 - 26n^3 + 76n^2 - 81n + 16)a[n-2]+(n-3)^4 n a[n-3])/((n-1)(n-4));
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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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