A006656 Denominators of expansion of sinh x / sin x. (Formerly M2294)

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

0,2

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.

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 *)

Prog

(Magma)
m:=120; R<x>:=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
(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

Crossrefs

Cf. A000965, A296628.

Sequence in context: A292953 A292221 A112534 * A367995 A205452 A159910

Adjacent sequences: A006653 A006654 A006655 * A006657 A006658 A006659

Keyword

nonn,easy,frac

Author

N. J. A. Sloane, Simon Plouffe

Extensions

More terms from Harvey P. Dale, Jul 10 2013

Status

approved