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

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

Author

N. J. A. Sloane, Apr 18 2005

Keywords

• sign
• frac

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

• Robert Israel, Table of n, a(n) for n = 0..2000

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 *)