A012476 - OEIS

%I #8 Oct 31 2013 04:33:27

%S 1,-5,65,-3005,278465,-42738005,9852460865,-3178878885005,

%T 1367383455547265,-756164182327284005,522662665715777337665,

%U -441523138107985704375005,447556468280585958726432065

%N arcsinh(cos(x)*sin(x))=x-5/3!*x^3+65/5!*x^5-3005/7!*x^7+278465/9!*x^9...

%F E.g.f.: log(sin(2*x)/2+sqrt(1+(sin(2*x))^2/4)). - _Vaclav Kotesovec_, Oct 31 2013

%F a(n) ~ (-1)^n * 5^(1/4) * 2^(4*n+3/2) * n^(2*n) / (exp(2*n)*(log(2+sqrt(5)))^(2*n+1/2)). - _Vaclav Kotesovec_, Oct 31 2013

%t Table[n!*SeriesCoefficient[ArcSinh[Cos[x]*Sin[x]],{x,0,n}],{n,1,40,2}] (* _Vaclav Kotesovec_, Oct 31 2013 *)

%K sign

%O 0,2

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