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%I #23 Jun 28 2015 10:28:03
%S 1,4,76,3592,325648,49088128,11155494208,3566506418560,
%T 1525463139748096,840688518856539136,579910469070833277952,
%U 489338149015716318963712,495775150805105569019662336
%N E.g.f.: arcsin(tan(sinh(x))) (odd powers only).
%C Series has radius of convergence arcsinh(Pi/4). It appears that
%C a(n) ~ c*(2n+1)!*arcsinh(Pi/4)^(-2n-1)/n^(3/2) for some constant c (approximately 0.3816). - _Robert Israel_, Jun 26 2015
%C c = 1/2*sqrt((1/2 + 16/(2*Pi*(Pi+sqrt(16+Pi^2))))*arcsinh(Pi/4)) = 0.3820437069654804064083... . - _Vaclav Kotesovec_, Jun 28 2015
%H Robert Israel, <a href="/A012155/b012155.txt">Table of n, a(n) for n = 0..200</a>
%e arcsin(tan(sinh(x))) = x + 4/3!*x^3 + 76/5!*x^5 + 3592/7!*x^7 + 325648/9!*x^9 + ...
%p S:= series(arcsin(tan(sinh(x))),x,102):
%p seq(coeff(S,x,2*j+1)*(2*j+1)!, j = 0 .. 50); # _Robert Israel_, Jun 26 2015
%t Select[ Range[0, 27]! CoefficientList[ Series[ ArcSin[ Tan[ Sinh[x]]], {x, 0, 27}], x], # > 0 &] (* _Robert G. Wilson v_, Jul 05 2005 *)
%K nonn
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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