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.
%I A296726 #27 Apr 30 2024 01:54:49
%S A296726 0,1,2,7,28,149,894,6483,51864,477801,4778010,53451135,641413620,
%T A296726 8446433085,118250063190,1792012416075,28672198657200,491536207523025,
%U A296726 8847651735414450,169292834944205175,3385856698884103500,71531660838216529125,1573696538440763640750
%N A296726 Expansion of e.g.f. arcsin(x)/(1 - x).
%H A296726 Muhammad Adam Dombrowski and Gregory Dresden, <a href="https://arxiv.org/abs/2404.17694">Areas Between Cosines</a>, arXiv:2404.17694 [math.CO], 2024.
%F A296726 E.g.f.: -i*log(i*x + sqrt(1 - x^2))/(1 - x), where i is the imaginary unit.
%F A296726 a(n) ~ n! * Pi/2. - _Vaclav Kotesovec_, Dec 20 2017
%F A296726 a(2*n) = 2*n*a(2*n-1). - _Greg Dresden_, Apr 04 2024
%F A296726 a(2*n+1) = (2*n+1)*(2*n)*a(2*n-1) + ((2*n-1)!!)^2, using the double factorial notation from A001147. - _Greg Dresden_, Apr 11 2024
%e A296726 arcsin(x)/(1 - x) = x/1! + 2*x^2/2! + 7*x^3/3! + 28*x^4/4! + 149*x^5/5! + ...
%p A296726 a:=series(arcsin(x)/(1 - x),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # _Paolo P. Lava_, Mar 27 2019
%t A296726 nmax = 22; CoefficientList[Series[ArcSin[x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%t A296726 nmax = 22; CoefficientList[Series[-I Log[I x + Sqrt[1 - x^2]]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%o A296726 (PARI) first(n) = x='x+O('x^n); Vec(serlaplace(asin(x)/(1 - x)), -n) \\ _Iain Fox_, Dec 19 2017
%Y A296726 Cf. A001147, A001818, A009551, A081358, A281964, A296727.
%K A296726 nonn
%O A296726 0,3
%A A296726 _Ilya Gutkovskiy_, Dec 19 2017