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A286175
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Sum of the n-th entries in all cycles of all permutations of [n+1].
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2
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4, 13, 43, 192, 1068, 7080, 54360, 473760, 4616640, 49714560, 586051200, 7504358400, 103703846400, 1538074137600, 24366332390400, 410609751552000, 7333437855744000, 138362409529344000, 2749819506610176000, 57416487392968704000, 1256593887223234560000
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OFFSET
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1,1
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LINKS
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FORMULA
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E.g.f.: -2*log(1-x)-(5*x^3-10*x^2+10*x-7)/(2*(1-x)^2)-7/2.
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EXAMPLE
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a(2) = 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, [4, 13][n],
(n-1)*(2*n^2+7*n+4)*a(n-1)/(2*n^2+3*n-1))
end:
seq(a(n), n=1..25);
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MATHEMATICA
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a[n_] := a[n] = If[n < 3, {4, 13}[[n]],
(n-1)*(2*n^2 + 7*n + 4)*a[n-1]/(2*n^2 + 3*n - 1)];
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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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