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%I #21 Sep 08 2022 08:45:29
%S 1,3,9,9,27,81,81,243,729,243,729,2187,2187,6561,19683,19683,59049,
%T 177147,59049,177147,531441,531441,1594323,4782969,4782969,14348907,
%U 43046721,4782969,14348907,43046721,43046721,129140163,387420489
%N Denominator of n!/3^n.
%H G. C. Greubel, <a href="/A125824/b125824.txt">Table of n, a(n) for n = 0..1000</a>
%F a(0)=1, a(3n+2) = 3^(n+2)*a(n), a(3n+1) = 3^(n+1)*a(n), a(3n) = 3^n*a(n).
%F a(n) = 3^A089792(n).
%F a(n) = denominator((1/(2*Pi)) * Integral_{t=0..2*Pi} exp(i*3*t)(-((Pi-t)/i)^n), i=sqrt(-1). - _Paul Barry_, Apr 02 2007
%t Table[Denominator[n!/3^n], {n,0,40}] (* _G. C. Greubel_, Aug 03 2019 *)
%o (PARI) a(n)=denominator(n!/3^n)
%o (Magma) [Denominator(Factorial(n)/3^n): n in [0..40]]; // _G. C. Greubel_, Aug 03 2019
%o (Sage) [denominator(factorial(n)/3^n) for n in (0..40)] # _G. C. Greubel_, Aug 03 2019
%o (GAP) List([0..40], n-> DenominatorRat(Factorial(n)/3^n) ); # _G. C. Greubel_, Aug 03 2019
%Y A212307 (numerators).
%K nonn,frac
%O 0,2
%A _Benoit Cloitre_, Feb 06 2007