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Expansion of e.g.f. arctan(sin(x)*log(x+1)).
1

%I #12 Sep 08 2022 08:44:38

%S 0,0,2,-3,4,-20,-130,1869,-12280,100080,-362822,-7482475,168953420,

%T -2715677172,34715587062,-205932278475,-3285394779888,157209810212416,

%U -4031590864355982,71565905502128781

%N Expansion of e.g.f. arctan(sin(x)*log(x+1)).

%H G. C. Greubel, <a href="/A012283/b012283.txt">Table of n, a(n) for n = 0..440</a>

%e E.g.f. = 2*x^2/2! - 3*x^3/3! + 4*x^4/4! - 20*x^5/5! + ...

%t CoefficientList[Series[ArcTan[Log[1 + x]*Sin[x]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Feb 05 2015 *)

%o (PARI) x='x+O('x^30); concat([0,0], Vec(serlaplace(atan(sin(x)* log(x+1))))) \\ _G. C. Greubel_, Oct 26 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arctan(Sin(x)*Log(x+1)) )); [0,0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // _G. C. Greubel_, Oct 26 2018

%K sign

%O 0,3

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

%E Prepended missing a(0)=a(1)=0 from _Vaclav Kotesovec_, Feb 05 2015