A125824 Denominator of n!/3^n.

1, 3, 9, 9, 27, 81, 81, 243, 729, 243, 729, 2187, 2187, 6561, 19683, 19683, 59049, 177147, 59049, 177147, 531441, 531441, 1594323, 4782969, 4782969, 14348907, 43046721, 4782969, 14348907, 43046721, 43046721, 129140163, 387420489

Offset: 0

Author

Benoit Cloitre, Feb 06 2007

Keywords

• nonn
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

A212307 (numerators).

Programs

GAP

List([0..40], n-> DenominatorRat(Factorial(n)/3^n) ); # G. C. Greubel, Aug 03 2019

Magma

[Denominator(Factorial(n)/3^n): n in [0..40]]; // G. C. Greubel, Aug 03 2019

Mathematica

Table[Denominator[n!/3^n], {n,0,40}] (* G. C. Greubel, Aug 03 2019 *)

PARI

a(n)=denominator(n!/3^n)

Sage

[denominator(factorial(n)/3^n) for n in (0..40)] # G. C. Greubel, Aug 03 2019

Formula

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).

a(n) = 3^A089792(n).

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