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1, 0, 3, -8, 25, -99, 721, -5704, 40881, -340325, 3628801, -41245511, 479001601, -6129725315, 87212177053, -1317906346184, 20922789888001, -354320889234597, 6402373705728001, -121882630320799633, 2432928081076384321, -51041048673495232715
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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The number of partitions of an n-set with distinct block sizes can
Möbius inversion yields: 1, -1, 2, -8, 24, -101, 720, -5696, 40878,...
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LINKS
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FORMULA
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a(n) = Sum_{d|n} -n!/(d*(-(n/d)!)^d).
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EXAMPLE
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a(6) = 1 - 10 + 30 - 120 = -99.
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MAPLE
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add(-n! / (d*(-(n/d)!)^d), d = numtheory[divisors](n)) end:
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MATHEMATICA
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a[n_] := Sum[ -n!/(d*(-(n/d)!)^d), {d, Divisors[n]}]; Table[a[n], {n, 1, 22}] // Flatten (* Jean-François Alcover, Jul 29 2013 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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