A012155 - OEIS

%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)