A047789 - OEIS

A047789

Denominators of Glaisher's I-numbers.

2, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 81, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3, 1

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OFFSET

0,1

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

J. W. L. Glaisher, On a set of coefficients analogous to the Eulerian numbers, Proc. London Math. Soc., 31 (1899), 216-235.

Index entries for sequences related to Glaisher's numbers

FORMULA

From Robert Israel, Aug 14 2018: (Start)

For n >= 1, a(3*n) = a(3*n+2) = 1 and a(3*n+1) = 3*a(n).

G.f. g(x) satisfies g(x) = 3*x*g(x^3) + 2 - 3*x + (x^2+x^3)/(1-x^3). (End)

EXAMPLE

1/2, 1/3, 1, 7, 809/9, 1847, 55601, 6921461/3,...

MAPLE

f:= n -> 3^padic:-ordp(2*n+1, 3):

f(0):= 2:

map(f, [$0..200]); # Robert Israel, Aug 14 2018

MATHEMATICA

a[0] = 2; a[n_] := 3^IntegerExponent[2n+1, 3];

Table[a[n], {n, 0, 101}] (* Jean-François Alcover, Feb 27 2019 *)

a[0]:=2; a[n_]:=Denominator[FunctionExpand[(PolyGamma[2*n, 1/3] + (3^(2*n+1)-1)*(2*n)!*Zeta[2*n+1]/2)*Sqrt[3]/(-2^(2*n)*Pi^(2*n+1))]]; Table[a[n], {n, 0, 100}] (* Detlef Meya, Sep 28 2024 *)

PROG

(PARI) a(n)=if(n<1, 2*(n==0), 3^valuation(2*n+1, 3)) /* Michael Somos, Feb 26 2004 */

(PARI) a(n)=if(n<1, 2*(n==0), n*=2; denominator(n!*polcoeff(3/(2+4*cos(x+O(x^n))), n))) /* Michael Somos, Feb 26 2004 */

CROSSREFS

Cf. A047788, A002111.

Sequence in context: A338072 A173272 A326303 * A068869 A251046 A064529

Adjacent sequences: A047786 A047787 A047788 * A047790 A047791 A047792

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

STATUS

approved