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%I #19 Apr 16 2018 10:14:01
%S 1,2,24,48,5760,1280,580608,1161216,1393459200,398131200,367873228800,
%T 363331584,24103053950976000,4382373445632000,115694658964684800,
%U 88995891511296000,726206474732175360000,6455168664286003200
%N Denominators of fractions appearing in a generalization of Carleman's inequality.
%H Steven R. Finch, <a href="/A219245/a219245.pdf">Carleman's inequality</a>, 2013. [Cached copy, with permission of the author]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CarlemansInequality.html">Carleman's Inequality</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Carleman's_inequality">Carleman's inequality</a>
%F b(0) = -1, b(n) = (-1/n)*sum_{k=1..n} b(n-k)/(k+1).
%e Fractions begin -1, 1/2, 1/24, 1/48, 73/5760, 11/1280, 3625/580608, ...
%t 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}]
%t 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 *)
%Y Cf. A249276 (numerators), A219245, A219246, A219336.
%K nonn,frac
%O 0,2
%A _Jean-François Alcover_, Oct 24 2014
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