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# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a047789 Showing 1-1 of 1 %I A047789 #24 Oct 23 2024 01:24:42 %S A047789 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, %T A047789 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, %U A047789 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 %N A047789 Denominators of Glaisher's I-numbers. %H A047789 Robert Israel, Table of n, a(n) for n = 0..10000 %H A047789 J. W. L. Glaisher, On a set of coefficients analogous to the Eulerian numbers, Proc. London Math. Soc., 31 (1899), 216-235. %H A047789 Index entries for sequences related to Glaisher's numbers %F A047789 From _Robert Israel_, Aug 14 2018: (Start) %F A047789 For n >= 1, a(3*n) = a(3*n+2) = 1 and a(3*n+1) = 3*a(n). %F A047789 G.f. g(x) satisfies g(x) = 3*x*g(x^3) + 2 - 3*x + (x^2+x^3)/(1-x^3). (End) %e A047789 1/2, 1/3, 1, 7, 809/9, 1847, 55601, 6921461/3,... %p A047789 f:= n -> 3^padic:-ordp(2*n+1,3): %p A047789 f(0):= 2: %p A047789 map(f, [$0..200]); # _Robert Israel_, Aug 14 2018 %t A047789 a[0] = 2; a[n_] := 3^IntegerExponent[2n+1, 3]; %t A047789 Table[a[n], {n, 0, 101}] (* _Jean-François Alcover_, Feb 27 2019 *) %t A047789 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 *) %o A047789 (PARI) a(n)=if(n<1,2*(n==0),3^valuation(2*n+1,3)) /* _Michael Somos_, Feb 26 2004 */ %o A047789 (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 */ %Y A047789 Cf. A047788, A002111. %K A047789 nonn,frac %O A047789 0,1 %A A047789 _N. J. A. Sloane_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE