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A108552
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Integer values of (1*2*...*k)/(1+2+...+k) = k!/T(k) = A000142(k)/A000217(k), k>=1.
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5
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1, 1, 8, 180, 1120, 8064, 604800, 68428800, 830269440, 10897286400, 2324754432000, 640237370572800, 11585247657984000, 221172909834240000, 93666727314800640000, 2068161339110798131200, 47726800133326110720000, 1148978521728221184000000, 28806532937614688256000000
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OFFSET
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1,3
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COMMENTS
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A000142(n)/A000217(n) = n!/(n*(n+1)/2) = 2*(n-1)!/(n+1) is an integer iff n = 1 or n + 1 is composite; i.e., iff n is a term of A060462.
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LINKS
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FORMULA
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MAPLE
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select(x-> denom(x)=1, [k!/(k*(k+1)/2)$k=1..30])[]; # Alois P. Heinz, Dec 11 2020
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MATHEMATICA
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Select[Table[(n - 1)!/((n (n - 1))/2), {n, 2, 50}], IntegerQ[#] &] (* Geoffrey Critzer, May 02 2015 *)
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PROG
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(PARI) for(n=1, 50, r=2*(n-1)!/(n+1); if(denominator(r)==1, print1(r, ", ")))
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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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