A202366 Approximate series expansion of arccosh(exp(3*x) - sin(3*x))

0, 6, 18, -36, -360, -1350, 27162, 337608, -606528, -90432450, -880859934, 18455713503, 693789107544, 1701104157090, -385899715094310, -8961561593356464, 131483054194960485, 11226865165557040813, 130224770734566143291, -10087278971257481285822

Offset

0,2

Comments

Inspired by the Demichel sequences.

Coefficients are multiplied by (n+1)! and rounded to the nearest integer. First fraction occurs at degree 11 ( 18455713503 = round(129189994524/7) ).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Example

arccosh(exp(3*x) - sin(3*x)) = 6*x/2! + 18*x^2/3! - 36*x^3/4! + ...

Mathematica

Round[Table[(i+1)!, {i, 0, 20}]*CoefficientList[Assuming[x > 0, Series[ArcCosh[Exp[3 x] - Sin[3 x]], {x, 0, 20}]], x]]

Crossrefs

Sequence in context: A225384 A276480 A180438 * A185223 A299272 A101853

Adjacent sequences: A202363 A202364 A202365 * A202367 A202368 A202369

Keyword

sign

Author

Olivier Gérard, Dec 18 2011

Status

approved