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A125562
a(n) = denominator of (2n + 1)!/3^n.
1
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, 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, 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
OFFSET
0,3
COMMENTS
Numerator of coefficients of sinh(sqrt(6*x))/sqrt(6*x). - Michael Somos, Aug 06 2017
LINKS
FORMULA
From Michael Somos, Aug 06 2017: (Start)
a(n) = 0 for all n < 0 is consistent with the following recurrences.
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)
EXAMPLE
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
MAPLE
A125562:=n->denom((2*n+1)!/3^n): seq(A125562(n), n=0..150); # Wesley Ivan Hurt, Aug 06 2017
MATHEMATICA
Table[Denominator[(2 n + 1)!/3^n], {n, 0, 96}] (* Michael De Vlieger, Jul 29 2017 *)
a[ n_] := Numerator[3^n / (2 n + 1)!]; (* Michael Somos, Aug 06 2017 *)
PROG
(PARI) a(n)=denominator((2*n+1)!/3^n)
(Python)
from sympy import factorial, Integer
def a(n): return (factorial(2*n + 1) / Integer(3)**n).denominator()
print([a(n) for n in range(51)]) # Indranil Ghosh, Jul 29 2017
(Magma) [Numerator((3^n / Factorial(2*n+1))): n in [0..90]]; // Vincenzo Librandi, Aug 08 2017
CROSSREFS
Sequence in context: A111629 A083953 A066400 * A337910 A092040 A293866
KEYWORD
nonn,frac
AUTHOR
Benoit Cloitre, Jan 01 2007
STATUS
approved