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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Numerator of coefficients of sinh(sqrt(6*x))/sqrt(6*x). - Michael Somos, Aug 06 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..19683

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

Adjacent sequences:  A125559 A125560 A125561 * A125563 A125564 A125565

KEYWORD

nonn,frac

AUTHOR

Benoit Cloitre, Jan 01 2007

STATUS

approved

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Last modified April 11 18:00 EDT 2021. Contains 342888 sequences. (Running on oeis4.)