A012572 - OEIS

%I #8 Oct 31 2013 04:40:45

%S 1,0,2,-3,16,-80,488,-3339,26472,-241128,2416002,-26168835,310984452,

%T -4057771068,56774212350,-841821751575,13356966503088,

%U -227284196307984,4085254725230514,-76911822855270819

%N exp(arcsinh(x)*log(x+1))=1+2/2!*x^2-3/3!*x^3+16/4!*x^4-80/5!*x^5...

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

%F a(n) ~ n! * (-1)^n * n^(log(1+sqrt(2))-1) / GAMMA(log(1+sqrt(2))). - _Vaclav Kotesovec_, Oct 31 2013

%t CoefficientList[Series[Exp[ArcSinh[x]*Log[x+1]], {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)