A012155 E.g.f.: arcsin(tan(sinh(x))) (odd powers only).

1, 4, 76, 3592, 325648, 49088128, 11155494208, 3566506418560, 1525463139748096, 840688518856539136, 579910469070833277952, 489338149015716318963712, 495775150805105569019662336

Offset

0,2

Comments

Series has radius of convergence arcsinh(Pi/4). It appears that

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 = 1/2*sqrt((1/2 + 16/(2*Pi*(Pi+sqrt(16+Pi^2))))*arcsinh(Pi/4)) = 0.3820437069654804064083... . - Vaclav Kotesovec, Jun 28 2015

Links

Robert Israel, Table of n, a(n) for n = 0..200

Example

arcsin(tan(sinh(x))) = x + 4/3!*x^3 + 76/5!*x^5 + 3592/7!*x^7 + 325648/9!*x^9 + ...

Maple

S:= series(arcsin(tan(sinh(x))), x, 102):
seq(coeff(S, x, 2*j+1)*(2*j+1)!, j = 0 .. 50); # Robert Israel, Jun 26 2015

Mathematica

Select[ Range[0, 27]! CoefficientList[ Series[ ArcSin[ Tan[ Sinh[x]]], {x, 0, 27}], x], # > 0 &] (* Robert G. Wilson v, Jul 05 2005 *)

Crossrefs

Sequence in context: A012080 A012047 A012010 * A350489 A325214 A118193

Adjacent sequences: A012152 A012153 A012154 * A012156 A012157 A012158

Keyword

nonn

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Status

approved