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

0,3

Links

Table of n, a(n) for n=0..23.

Formula

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

Example

-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! + ...

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]!

Prog

(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

Crossrefs

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

Sequence in context: A012352 A012704 A012698 * A012355 A012353 A012703

Adjacent sequences: A302608 A302609 A302610 * A302612 A302613 A302614

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 10 2018

Status

approved