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%I #11 Oct 18 2012 06:00:36
%S 0,6,18,-36,-360,-1350,27162,337608,-606528,-90432450,-880859934,
%T 18455713503,693789107544,1701104157090,-385899715094310,
%U -8961561593356464,131483054194960485,11226865165557040813,130224770734566143291,-10087278971257481285822
%N Approximate series expansion of arccosh(exp(3*x) - sin(3*x))
%C Inspired by the Demichel sequences.
%C Coefficients are multiplied by (n+1)! and rounded to the nearest integer. First fraction occurs at degree 11 ( 18455713503 = round(129189994524/7) ).
%H Vincenzo Librandi, <a href="/A202366/b202366.txt">Table of n, a(n) for n = 0..100</a>
%e arccosh(exp(3*x) - sin(3*x)) = 6*x/2! + 18*x^2/3! - 36*x^3/4! + ...
%t Round[Table[(i+1)!, {i, 0, 20}]*CoefficientList[Assuming[x > 0, Series[ArcCosh[Exp[3 x] - Sin[3 x]], {x, 0, 20}]], x]]
%K sign
%O 0,2
%A _Olivier Gérard_, Dec 18 2011
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