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

0,2

Links

Table of n, a(n) for n=0..17.

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: A073215 A111035 A349188 * A002552 A075265 A053657

Adjacent sequences: A249274 A249275 A249276 * A249278 A249279 A249280

Keyword

nonn,frac

Author

Jean-François Alcover, Oct 24 2014

Status

approved