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Expansion of e.g.f.: x*cos(log(1+x)).
6

%I #22 Sep 08 2022 08:44:37

%S 0,1,0,-3,12,-50,240,-1330,8400,-59580,468000,-4018300,37237200,

%T -367507400,3802780800,-40373385000,423927504000,-4048235126000,

%U 25093796832000,288695417426000,-18721925937000000,623644389813900000

%N Expansion of e.g.f.: x*cos(log(1+x)).

%H G. C. Greubel, <a href="/A009024/b009024.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) = n * A003703(n-1).

%F a(n+3) = -a(n+2)*(2*n+1)*(n+3)/(n+2) - a(n+1)*(1+n^2)*(n+3)/(n+1), a(0)=0, a(1)=1, a(2)=0. - _Sergei N. Gladkovskii_, Aug 17 2012

%t With[{nmax = 30}, CoefficientList[Series[x*Cos[Log[1 + x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 22 2018 *)

%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(x*cos(log(1+x))))) \\ _G. C. Greubel_, Jul 22 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:= [0] cat Coefficients(R!(x*Cos(Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 22 2018

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997