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A012584 exp(arcsinh(x)*exp(x))=1+x+3/2!*x^2+9/3!*x^3+33/4!*x^4+145/5!*x^5... 1

%I #8 Oct 31 2013 05:23:43

%S 1,1,3,9,33,145,715,3801,21889,140001,974803,6947017,50720417,

%T 421135793,3950147227,33562929817,240061039105,2672302901185,

%U 45695167547043,388308372326665,-1858226878271967,9709607588675537

%N exp(arcsinh(x)*exp(x))=1+x+3/2!*x^2+9/3!*x^3+33/4!*x^4+145/5!*x^5...

%F E.g.f.: (x+sqrt(1+x^2))^(exp(x)). - _Vaclav Kotesovec_, Oct 31 2013

%F a(n) ~ 2*sin(n*Pi/2-1-Pi*cos(1)/2) * exp(-Pi*sin(1)/2) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Oct 31 2013

%t CoefficientList[Series[Exp[ArcSinh[x]*Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 31 2013 *)

%K sign

%O 0,3

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

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Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)