cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A006656 Denominators of expansion of sinh x / sin x.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Simon Plouffe

Keywords

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

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

A024342 Expansion of e.g.f. tanh(x)*tan(x), coefficients of powers x^(4*n+2).

Original entry on oeis.org

2, 112, 92672, 365688832, 4411282030592, 127206964253949952, 7496936195881447718912, 809926025985929119868649472, 148071124873925782667263194693632, 43087047288444223765736160658186043392, 19011875896715283767147325248912471990730752
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A000182, A009837, A296628.

Programs

  • Magma
    m:=50; R:=PowerSeriesRing(Rationals(), m);
b:= Coefficients(R!(Laplace( Tan(x)*Tanh(x) )));
[b[4*n-3]: n in [1..Floor((m-2)/4)]]; // G. C. Greubel, Jan 31 2022
  • Mathematica
    With[{nn=40},Take[CoefficientList[Series[Tanh[x]Tan[x],{x,0,nn}], x] Range[0,nn-2]!,{3,-1,4}]] (* Harvey P. Dale, May 02 2012 *)
  • Sage
    [factorial(4*n+2)*( tanh(x)*tan(x) ).series(x, 4*n+3).list()[4*n+2] for n in (0..20)] # G. C. Greubel, Jan 31 2022

Formula

a(n) = 2 * A009837(n).

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997
More terms from Harvey P. Dale, May 02 2012
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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