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.

A296789 Expansion of e.g.f. exp(x*arctanh(x)) (even powers only).

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%I A296789 #6 Dec 21 2017 06:07:25
%S A296789 1,2,20,504,24464,1959840,234852672,39370660224,8799246209280,
%T A296789 2528787321598464,908585701684024320,399070678264750356480,
%U A296789 210373049449102957645824,131083661069772517440921600,95304505860052894815543705600,79961055068441273887848131297280
%N A296789 Expansion of e.g.f. exp(x*arctanh(x)) (even powers only).
%F A296789 a(n) = (2*n)! * [x^(2*n)] exp(x*arctanh(x)).
%F A296789 a(n) ~ 2^(2*n + 2) * n^(2*n) / exp(2*n). - _Vaclav Kotesovec_, Dec 21 2017
%e A296789 exp(x*arctanh(x)) = 1 + 2*x^2/2! + 20*x^4/4! + 504*x^6/6! + 24464*x^8/8! + ...
%t A296789 nmax = 15; Table[(CoefficientList[Series[Exp[x ArcTanh[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
%t A296789 nmax = 15; Table[(CoefficientList[Series[Exp[x (Log[1 + x] - Log[1 - x])/2], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
%Y A296789 Cf. A000246, A009252, A009273, A010050, A166356, A259647, A293193, A296787, A296788.
%K A296789 nonn
%O A296789 0,2
%A A296789 _Ilya Gutkovskiy_, Dec 20 2017