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%I #30 Sep 08 2022 08:45:28
%S 1,1,3,3,1,3,3,3,9,3,3,9,9,1,3,3,3,9,3,3,9,9,3,9,9,9,27,3,3,9,9,3,9,9,
%T 9,27,9,9,27,27,1,3,3,3,9,3,3,9,9,3,9,9,9,27,3,3,9,9,3,9,9,9,27,9,9,
%U 27,27,3,9,9,9,27,9,9,27,27,9,27,27,27,81,3,3,9,9,3,9,9,9,27,9,9,27,27,3,9,9
%N a(n) = denominator of (2n + 1)!/3^n.
%C Numerator of coefficients of sinh(sqrt(6*x))/sqrt(6*x). - _Michael Somos_, Aug 06 2017
%H Antti Karttunen, <a href="/A125562/b125562.txt">Table of n, a(n) for n = 0..19683</a>
%F From _Michael Somos_, Aug 06 2017: (Start)
%F a(n) = 0 for all n < 0 is consistent with the following recurrences.
%F a(3*n + 1) = a(n), a(3*n + 2) = 3*a(n), a(9*n) = a(3*n), a(9*n + 3) = a(9*n + 6) = 3*a(n) for all n in Z. (End)
%e sinh(sqrt(6*x))/sqrt(6*x) = 1 + 1*x^1 + 3*x^2/10 + 3*x^3/70 + 1*x^4/280 + 3*x^5/15400 + ... - _Michael Somos_, Aug 06 2017
%p A125562:=n->denom((2*n+1)!/3^n): seq(A125562(n), n=0..150); # _Wesley Ivan Hurt_, Aug 06 2017
%t Table[Denominator[(2 n + 1)!/3^n], {n, 0, 96}] (* _Michael De Vlieger_, Jul 29 2017 *)
%t a[ n_] := Numerator[3^n / (2 n + 1)!]; (* _Michael Somos_, Aug 06 2017 *)
%o (PARI) a(n)=denominator((2*n+1)!/3^n)
%o (Python)
%o from sympy import factorial, Integer
%o def a(n): return (factorial(2*n + 1) / Integer(3)**n).denominator()
%o print([a(n) for n in range(51)]) # _Indranil Ghosh_, Jul 29 2017
%o (Magma) [Numerator((3^n / Factorial(2*n+1))): n in [0..90]]; // _Vincenzo Librandi_, Aug 08 2017
%K nonn,frac
%O 0,3
%A _Benoit Cloitre_, Jan 01 2007
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