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A097303 Denominators in Stirling's asymptotic series.

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%I A097303 #15 Sep 23 2022 17:20:13
%S A097303 1,12,144,8640,103680,1741824,104509440,179159040,2149908480,
%T A097303 1418939596800,23838185226240,338068808663040,20284128519782400,
%U A097303 18723810941337600,32097961613721600,229179445921972224000
%N A097303 Denominators in Stirling's asymptotic series.
%C A097303 Numerators coincide with the numbers depicted in A001163 but differ for the first time at entry nr. 33. See the W. Lang link.
%C A097303 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.
%H A097303 W. Lang, <a href="/A097303/a097303.txt">More terms and comments</a>.
%F A097303 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).
%t A097303 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 *)
%Y A097303 Cf. A001163, A001164 (Stirling formula with further links and references.).
%K A097303 nonn,easy
%O A097303 0,2
%A A097303 _Wolfdieter Lang_, Aug 13 2004