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%I #17 Jan 29 2018 02:54:05
%S 1,0,1,-4,9,-40,385,-2700,15505,-145360,1886625,-19796500,190881625,
%T -2654379000,44269902625,-625468889500,8553276590625,-156119043652000,
%U 3194978818578625,-57041478987070500
%N Expansion of e.g.f. exp(arctan(x) - log(x+1)).
%H Robert Israel, <a href="/A013459/b013459.txt">Table of n, a(n) for n = 0..449</a>
%F From _Robert Israel_, Jan 29 2018: (Start)
%F E.g.f.: exp(arctan(x) - log(x+1)).
%F (n+1)^2*(n+2)*a(n)+n*(n+2)*a(n+1)+(n+2)*a(n+2)+a(n+3) = 0. (End)
%p f:= gfun:-rectoproc({(n+1)^2*(n+2)*a(n)+n*(n+2)*a(n+1)+(n+2)*a(n+2)+a(n+3) = 0, a(0)=1,a(1)=0,a(2)=1}, a(n), remember):
%p map(f, [$0..40]); # _Robert Israel_, Jan 29 2018
%t With[{nn=20},CoefficientList[Series[Exp[ArcTan[x]-Log[x+1]],{x,0,nn}], x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 03 2011 *)
%o (PARI) a(n)=polcoeff(exp(atan(x))/(1+x),n)*n! \\ _Jaume Oliver Lafont_, Oct 24 2009
%K sign
%O 0,4
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Edited by _Robert Israel_, Jan 29 2018