A006656 Denominators of expansion of sinh x / sin x.

1, 3, 3, 21, 9, 11, 21, 9, 1, 133, 693, 69, 7, 189, 3, 7161, 231, 7, 399, 63, 77, 3311, 4347, 987, 49, 33, 33, 627, 57, 59, 7161, 2079, 11, 10787, 207, 2343, 1463, 4389, 231, 1659, 6237, 913, 9933, 693, 161, 7301833, 19184319, 4389, 11, 99, 33

Offset: 0

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn
• easy
• frac

Comments

Also denominators of the expansion of tan(x)/tanh(x). - G. C. Greubel, Jan 31 2022

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• J. M. Gandhi, The coefficients of cosh x/cos x and a note on Carlitz's coefficients of sinh x/sin x, Math. Mag., 31 (1958), 185-191.

Crossrefs

Cf. A000965, A296628.

Programs

Magma

m:=120; R:=PowerSeriesRing(Rationals(), m);
b:= Coefficients(R!(Laplace( Sinh(x)/Sin(x) )));
[Denominator( b[2*n-1] ): n in [1..Floor((m-2)/2)]]; // G. C. Greubel, Jan 31 2022

Mathematica

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 *)

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

Extensions

More terms from Harvey P. Dale, Jul 10 2013