%I #10 Mar 27 2019 03:51:58

%S 0,0,2,3,16,50,368,1764,16896,109584,1297152,10628640,149944320,

%T 1486442880,24349317120,283465647360,5287713177600,70734282393600,

%U 1480103564083200,22376988058521600,519000166327910400,8752948036761600000,222845873874075648000,4148476779335454720000

%N Expansion of e.g.f. -log(1 - x)*arctanh(x).

%F E.g.f.: log(1 - x)*log((1 - x)/(1 + x))/2.

%e -log(1 - x)*arctanh(x) = 2*x^2/2! + 3*x^3/3! + 16*x^4/4! + 50*x^5/5! + 368*x^6/6! + 1764*x^7/7! + 16896*x^8/8! + ...

%p a:=series(-log(1-x)*arctanh(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 - x] ArcTanh[x], {x, 0, nmax}], x] Range[0, nmax]!

%o (PARI) x='x+O('x^99); concat([0, 0], Vec(serlaplace(log(1-x)*log((1-x)/(1+x))/2))) \\ _Altug Alkan_, Apr 10 2018

%Y Cf. A005359, A009410, A009416, A009429, A009435, A012697, A081358, A104150, A177699, A177700, A202139, A302610.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 10 2018