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 A127588 Maximal numerator of Product[(k/(k+1))^e(k),{k,1,n}] over all exponents e(k) equal to either 1 or -1. 0
 2, 4, 16, 64, 128, 576, 4608, 16384, 64000, 640000, 2560000, 10240000, 54080000, 135200000, 1554251776, 24868028416, 49736056832, 557256278016, 2244339564544, 11075584000000, 74331795750912, 936622443986944 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES R. de la Bret`eche, C. Pomerance and G. Tenenbaum, Products of ratios of consecutive integers, Ramanujan J. 9 (2005) 131-138 J.-L. Nicolas, Nombres hautement compos'es, Acta Arith. 49 (1988) 395-412 J.-L. Nicolas, Some open questions, Ramanujan J. 9 (2005) 251-264 LINKS S. R. Finch, Products of consecutive-integer ratios. EXAMPLE For n=6, (1/2)^(-1)*(2/3)^(-1)*(3/4)^(-1)*(4/5)*(5/6)^(-1)*(6/7) has, of all such products, the largest numerator 576. CROSSREFS For the corresponding denominators see A001902. Sequence in context: A138868 A138871 A001901 * A187822 A092585 A106186 Adjacent sequences:  A127585 A127586 A127587 * A127589 A127590 A127591 KEYWORD nonn AUTHOR Steven Finch, Apr 17 2007 EXTENSIONS More terms from Robert G. Wilson v, Apr 24 2007 STATUS approved

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