A097303 - OEIS

A097303

Denominators in Stirling's asymptotic series.

1, 12, 144, 8640, 103680, 1741824, 104509440, 179159040, 2149908480, 1418939596800, 23838185226240, 338068808663040, 20284128519782400, 18723810941337600, 32097961613721600, 229179445921972224000

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OFFSET

0,2

COMMENTS

Numerators coincide with the numbers depicted in A001163 but differ for the first time at entry nr. 33. See the W. Lang link.

Stirling's formula for Gamma(z) (|arg(z)| < Pi) uses the asymptotic series Sum_{k>=0} (N(k)/a(k))*((1/z)^k)/k!. For N(k) see the W. Lang link.

LINKS

Table of n, a(n) for n=0..15.

W. Lang, More terms and comments.

FORMULA

a(n) = denominator(s(n)), where the signed rationals s(n) are the coefficients of ((1/z)^k)/k! in the asymptotic series appearing in Stirling's formula for Gamma(z).

MATHEMATICA

max = 15; se = Series[(E^x*Sqrt[1/x]*Gamma[x+1])/(x^x*Sqrt[2*Pi]), {x, Infinity, max}]; Denominator[ CoefficientList[ se /. x -> 1/x, x]*Range[0, max]!] (* Jean-François Alcover, Nov 03 2011 *)

CROSSREFS

Cf. A001163, A001164 (Stirling formula with further links and references.).

Sequence in context: A143248 A138444 A137886 * A067219 A075619 A055332

Adjacent sequences: A097300 A097301 A097302 * A097304 A097305 A097306

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 13 2004

STATUS

approved