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A123931
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a(n) = H(n)*n!/(floor(n/2))! (mod (n+1)), where H(n) = sum{k=1 to n} 1/k, the n-th harmonic number.
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1
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0, 1, 0, 3, 0, 5, 0, 2, 3, 4, 0, 0, 0, 6, 9, 0, 0, 0, 0, 0, 18, 10, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 30, 16, 0, 0, 0, 18, 24, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 54, 28, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 42, 51, 0, 0, 0, 0, 0, 3, 46, 0, 0, 0
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OFFSET
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0,4
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LINKS
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MATHEMATICA
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f[n_]:= Mod[HarmonicNumber[n]n!/Floor[n/2]!, n + 1]; Table[f[n], {n, 0, 100}] (* Ray Chandler, Dec 11 2006 *)
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PROG
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(PARI) a(n) = (n!*sum(k=1, n, 1/k)/(n\2)!)%(n+1);
(Sage) [mod(harmonic_number(n)*factorial(n)/factorial(floor(n/2)), n+1) for n in (0..100)] # G. C. Greubel, Aug 05 2019
(GAP)List([0..100], n-> (Factorial(n)*Sum([1..n], k-> 1/k)/Factorial(Int(n/2))) mod (n+1) ); # G. C. Greubel, Aug 05 2019
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CROSSREFS
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KEYWORD
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easy,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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