cp's OEIS Frontend

A006656 Denominators of expansion of sinh x / sin x.

%I A006656 M2294 #27 Feb 03 2022 06:01:14
%S A006656 1,3,3,21,9,11,21,9,1,133,693,69,7,189,3,7161,231,7,399,63,77,3311,
%T A006656 4347,987,49,33,33,627,57,59,7161,2079,11,10787,207,2343,1463,4389,
%U A006656 231,1659,6237,913,9933,693,161,7301833,19184319,4389,11,99,33
%N A006656 Denominators of expansion of sinh x / sin x.
%C A006656 Also denominators of the expansion of tan(x)/tanh(x). - _G. C. Greubel_, Jan 31 2022
%D A006656 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006656 G. C. Greubel, <a href="/A006656/b006656.txt">Table of n, a(n) for n = 0..1000</a>
%H A006656 J. M. Gandhi, <a href="http://www.jstor.org/stable/3029194">The coefficients of cosh x/cos x and a note on Carlitz's coefficients of sinh x/sin x</a>, Math. Mag., 31 (1958), 185-191.
%t A006656 With[{nn=100},Denominator[Take[CoefficientList[Series[Sinh[x]/Sin[x],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]]] (* _Harvey P. Dale_, Jul 10 2013 *)
%o A006656 (Magma)
%o A006656 m:=120; R<x>:=PowerSeriesRing(Rationals(), m);
%o A006656 b:= Coefficients(R!(Laplace( Sinh(x)/Sin(x) )));
%o A006656 [Denominator( b[2*n-1] ): n in [1..Floor((m-2)/2)]]; // _G. C. Greubel_, Jan 31 2022
%o A006656 (Sage) [denominator( factorial(2*n)*( sinh(x)/sin(x) ).series(x, 2*n+3).list()[2*n] ) for n in (0..60)] # _G. C. Greubel_, Jan 31 2022
%Y A006656 Cf. A000965, A296628.
%K A006656 nonn,easy,frac
%O A006656 0,2
%A A006656 _N. J. A. Sloane_, _Simon Plouffe_
%E A006656 More terms from _Harvey P. Dale_, Jul 10 2013