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.

A098087 Numerators of coefficients in expansion of x^2*(1-exp(-2*x))^(-2).

Original entry on oeis.org

1, 1, 5, 1, 1, -1, -1, 1, 1, -1, -1, 1, 691, -691, -1, 2, 3617, -3617, -43867, 43867, 174611, -174611, -77683, 155366, 236364091, -236364091, -657931, 1315862, 3392780147, -6785560294, -3446336510402, 6892673020804, 7709321041217, -7709321041217, -151628697551, 151628697551
Offset: 0

Views

Author

N. J. A. Sloane, Apr 17 2005

Keywords

Comments

Suggested by Bill Gosper's remarkable identity (in a posting to math-fun list, Apr 14 2005) (replace dots by spaces to make this more visible): Product_{ n >= 0 } tanh(2^n x)^(1/2^n) = (1-exp(-2*x))^2.

Crossrefs

Cf. A104007, A104042, A104097.

A104042 Numerators of coefficients in expansion of x^-2*(1-exp(-2*x))^2.

Original entry on oeis.org

4, -8, 28, -8, 248, -16, 508, -136, 584, -496, 16376, -16, 131056, -174752, 18724, -2056, 1048568, -1168, 4194296, -20336, 684784, -1945184, 67108856, -3856, 536870896, -715827872, 306783376, -19746976, 17179869152, -3198784, 8589934588, -134744072, 426829048, -91625968976
Offset: 0

Views

Author

N. J. A. Sloane, Apr 18 2005

Keywords

Comments

Suggested by Bill Gosper's remarkable identity (in a posting to math-fun list, Apr 14 2005): Product_{ n >= 0 } tanh(2^n x)^(1/2^n) = (1-exp(-2*x))^2.

Links

Crossrefs

Cf. A104097, A104007, A104042.

Programs

  • Maple
    S:= series(x^(-2)*(1-exp(-2*x))^2, x, 34):
seq(numer(coeff(S,x,j)),j=0..31); # Robert Israel, Aug 12 2019
  • Mathematica
    Numerator[ CoefficientList[ Series[x^-2*(1 - E^(-2x))^2, {x, 0, 33}], x]] (* Robert G. Wilson v, Apr 20 2005 *)
Showing 1-2 of 2 results.

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

Content is available under The OEIS End-User License Agreement.