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A108552
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Integer values of (1*2*...*n)/(1+2+...+n) = n!/T(n) = A000142(n)/A000217(n), n>=1.
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4
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1, 1, 8, 180, 1120, 8064, 604800, 68428800, 830269440, 10897286400, 2324754432000, 640237370572800, 11585247657984000, 221172909834240000, 93666727314800640000, 2068161339110798131200, 47726800133326110720000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Factorial numbers (*) and triangular numbers (+) both operate on 1,2,...,n. 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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FORMULA
| a(m) = 2*(A060462(m)-1)!/(A060462(m)+1) = A000142(A060462(m))/A000217(A060462(m)), m>=0.
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PROG
| (PARI) for(n=1, 50, r=2*(n-1)!/(n+1); if(denominator(r)==1, print1(r, ", ")))
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CROSSREFS
| Cf. A060462 (corresponding n), A000142 (factorials), A000217 (triangular numbers).
Sequence in context: A001596 A159326 A089456 * A060593 A130775 A203359
Adjacent sequences: A108549 A108550 A108551 * A108553 A108554 A108555
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KEYWORD
| nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 09 2005
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