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A047789 Denominators of Glaisher's I-numbers. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
J. W. L. Glaisher, On a set of coefficients analogous to the Eulerian numbers, Proc. London Math. Soc., 31 (1899), 216-235.
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 *)
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
Sequence in context: A338072 A173272 A326303 * A068869 A251046 A064529
KEYWORD
nonn,frac
AUTHOR
STATUS
approved

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Last modified February 24 10:26 EST 2024. Contains 370294 sequences. (Running on oeis4.)