cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A302611 #10 Mar 27 2019 03:51:58
%S A302611 0,0,2,3,16,50,368,1764,16896,109584,1297152,10628640,149944320,
%T A302611 1486442880,24349317120,283465647360,5287713177600,70734282393600,
%U A302611 1480103564083200,22376988058521600,519000166327910400,8752948036761600000,222845873874075648000,4148476779335454720000
%N A302611 Expansion of e.g.f. -log(1 - x)*arctanh(x).
%F A302611 E.g.f.: log(1 - x)*log((1 - x)/(1 + x))/2.
%e A302611 -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 A302611 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 A302611 nmax = 23; CoefficientList[Series[-Log[1 - x] ArcTanh[x], {x, 0, nmax}], x] Range[0, nmax]!
%o A302611 (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 A302611 Cf. A005359, A009410, A009416, A009429, A009435, A012697, A081358, A104150, A177699, A177700, A202139, A302610.
%K A302611 nonn
%O A302611 0,3
%A A302611 _Ilya Gutkovskiy_, Apr 10 2018