A154268 Ratios of consecutive denominators of Stirling's expansion for the Gamma function.

12, 24, 180, 48, 84, 360, 12, 96, 5940, 168, 156, 720, 12, 24, 107100, 192, 228, 11880, 12, 336, 4140, 312, 12, 1440, 84, 24, 516780, 48, 372, 214200, 12

Offset: 0

Author

Paul Curtz, Jan 06 2009

Keywords

• nonn
• fini
• full

Comments

The sequence is finite because the ratios are no longer integer after a(30).

All entries are multiples of 12.

a(n) mod 9 is one of {0,3,6}.

Programs

Mathematica

dd = Denominator[ CoefficientList[ Normal[ Series[ E^x*x^(x-1/2)*x! / Sqrt[2*Pi], {x, Infinity, 31}]] /. x -> 1/x, x]]; Rest[ dd / RotateRight[dd] ] (* Jean-François Alcover, Aug 03 2012 *)

Formula

a(n) = A001164(n+1)/A001164(n).

Extensions

Edited and extended by R. J. Mathar, Sep 07 2009