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 A249277 Denominators of fractions appearing in a generalization of Carleman's inequality. 1
 1, 2, 24, 48, 5760, 1280, 580608, 1161216, 1393459200, 398131200, 367873228800, 363331584, 24103053950976000, 4382373445632000, 115694658964684800, 88995891511296000, 726206474732175360000, 6455168664286003200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Steven R. Finch, Carleman's inequality, 2013. [Cached copy, with permission of the author] Eric Weisstein's World of Mathematics, Carleman's Inequality Wikipedia, Carleman's inequality FORMULA b(0) = -1, b(n) = (-1/n)*sum_{k=1..n} b(n-k)/(k+1). EXAMPLE Fractions begin -1, 1/2, 1/24, 1/48, 73/5760, 11/1280, 3625/580608, ... MATHEMATICA b[0] = -1; b[n_] := b[n] = (-1/n)*Sum[b[n - k]/(k + 1), {k, 1, n}]; Table[b[n] // Denominator, {n, 0, 20}] CoefficientList[Series[-(1 - x)^((x - 1)/x)/E, {x, 0, 20}], x] // Denominator (* communicated by Eric W. Weisstein, Apr 13 2018, based on result by Michael Trott *) CROSSREFS Cf. A249276 (numerators), A219245, A219246, A219336. Sequence in context: A181283 A073215 A111035 * A002552 A075265 A053657 Adjacent sequences:  A249274 A249275 A249276 * A249278 A249279 A249280 KEYWORD nonn,frac AUTHOR Jean-François Alcover, Oct 24 2014 STATUS approved

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Last modified September 19 17:22 EDT 2020. Contains 337178 sequences. (Running on oeis4.)