A097303 Denominators in Stirling's asymptotic series.

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

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