%I #7 Mar 27 2019 03:51:10
%S 0,1,-3,6,-8,13,-103,462,824,-8239,-147747,1233518,12148288,
%T -127674419,-2090702391,24495009510,410685350032,-5514147250815,
%U -111860639828131,1673006899192118,37306857729115304,-619246417449233555,-15476404474443728487,281907759055194714206
%N Expansion of e.g.f. log(1 + arctan(x))*exp(-x).
%e log(1 + arctan(x))*exp(-x) = x/1! - 3*x^2/2! + 6*x^3/3! - 8*x^4/4! + 13*x^5/5! - 103*x^6/6! + ...
%p a:=series(log(1+arctan(x))*exp(-x),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # _Paolo P. Lava_, Mar 26 2019
%t nmax = 23; CoefficientList[Series[Log[1 + ArcTan[x]] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 23; CoefficientList[Series[Log[1 + (I/2) (Log[1 - I x] - Log[1 + I x])] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A009337, A009356, A009374, A009393, A110708, A296438, A297209, A297210, A297213.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Dec 27 2017