A302611 Expansion of e.g.f. -log(1 - x)*arctanh(x).

0, 0, 2, 3, 16, 50, 368, 1764, 16896, 109584, 1297152, 10628640, 149944320, 1486442880, 24349317120, 283465647360, 5287713177600, 70734282393600, 1480103564083200, 22376988058521600, 519000166327910400, 8752948036761600000, 222845873874075648000, 4148476779335454720000

Offset: 0

Author

Ilya Gutkovskiy, Apr 10 2018

Keywords

• nonn

Examples

			-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! + ...
		

Crossrefs

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

Programs

Maple

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

Mathematica

nmax = 23; CoefficientList[Series[-Log[1 - x] ArcTanh[x], {x, 0, nmax}], x] Range[0, nmax]!

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

Formula

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