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%I #10 Aug 12 2019 16:35:25
%S 4,-8,28,-8,248,-16,508,-136,584,-496,16376,-16,131056,-174752,18724,
%T -2056,1048568,-1168,4194296,-20336,684784,-1945184,67108856,-3856,
%U 536870896,-715827872,306783376,-19746976,17179869152,-3198784,8589934588,-134744072,426829048,-91625968976
%N Numerators of coefficients in expansion of x^-2*(1-exp(-2*x))^2.
%C 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.
%H Robert Israel, <a href="/A104042/b104042.txt">Table of n, a(n) for n = 0..2000</a>
%p S:= series(x^(-2)*(1-exp(-2*x))^2, x, 34):
%p seq(numer(coeff(S,x,j)),j=0..31); # _Robert Israel_, Aug 12 2019
%t Numerator[ CoefficientList[ Series[x^-2*(1 - E^(-2x))^2, {x, 0, 33}], x]] (* _Robert G. Wilson v_, Apr 20 2005 *)
%Y Cf. A104097, A104007, A104042.
%K sign,frac
%O 0,1
%A _N. J. A. Sloane_, Apr 18 2005