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A069839
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Number of different (unlabeled) 2-cell embeddings of the complete graph K_n on n vertices into orientable surfaces.
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1
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1, 1, 1, 3, 78, 265764, 71095150000, 1791180894322714050, 5782448787773327324756945480, 3129263982719398327413605440811466528960, 359946241929477448403523246795300556527932947115524992
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n)=sum_(d|n) (n-2)!^(n/d)/(d^(n/d)*(n/d)!)+ sum_(d|n-1, d>1) phi(d)*(n-2)!^((n-1)/d))/(n-1), n>1, where phi(n) is the Euler totient function A000010.
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MATHEMATICA
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f[n_] := Block[{d = Divisors[n], d1 = Drop[ Divisors[n - 1], 1]}, Apply[ Plus, (n - 2)!^(n/d)/(d^(n/d)*(n/d)!)] + Apply[ Plus, EulerPhi[d1]*(n - 2)!^((n - 1)/d1)/(n - 1)]]; f[1] = 1; Table[ f[n], {n, 2, 13}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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