A249277 Denominators of fractions appearing in a generalization of Carleman's inequality.

1, 2, 24, 48, 5760, 1280, 580608, 1161216, 1393459200, 398131200, 367873228800, 363331584, 24103053950976000, 4382373445632000, 115694658964684800, 88995891511296000, 726206474732175360000, 6455168664286003200

Offset: 0

Author

Jean-François Alcover, Oct 24 2014

Keywords

• nonn
• frac

Examples

			Fractions begin -1, 1/2, 1/24, 1/48, 73/5760, 11/1280, 3625/580608, ...
		

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

Crossrefs

Cf. A249276 (numerators), A219245, A219246, A219336.

Programs

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 *)

Formula

b(0) = -1, b(n) = (-1/n)*sum_{k=1..n} b(n-k)/(k+1).