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 A166741 #14 Nov 06 2014 15:02:21 %S A166741 1,2,4,10,32,130,640,3770,25600,199810,1740800,16983850,181043200, %T A166741 2122981250,26794393600,367275756250,5358878720000,84106148181250, %U A166741 1393308467200000,24643101417106250,457005177241600000 %N A166741 E.g.f.: exp(2*arcsin(x)). %C A166741 exp(2*arcsin(1)) is Aleksandr Gelfond's constant. %H A166741 Wikipedia, <a href="http://en.wikipedia.org/wiki/Gelfond's_constant">Gelfond's constant</a> %F A166741 a(n) ~ 2 * n^(n-1) * (exp(Pi) - (-1)^n/exp(Pi)) / exp(n). - _Vaclav Kotesovec_, Aug 04 2014 %F A166741 From _Vaclav Kotesovec_, Nov 06 2014: (Start) %F A166741 a(n) = (n^2 - 4*n + 8)*a(n-2). %F A166741 a(n) = 2^(n-1) * (exp(Pi)-(-1)^n*exp(-Pi)) * GAMMA(n/2-I) * GAMMA(n/2+I) / Pi. %F A166741 (End) %p A166741 seq(simplify(2^(n-1) * (cosh(Pi)*(1-(-1)^n) + sinh(Pi)*(1+(-1)^n)) * GAMMA((1/2)*n-I)*GAMMA((1/2)*n+I) / Pi), n=0..20); # _Vaclav Kotesovec_, Nov 06 2014 %t A166741 CoefficientList[Series[E^(2*ArcSin[x]), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Aug 04 2014 *) %t A166741 FullSimplify[Table[2^(n-1) * (E^(Pi)-(-1)^n*E^(-Pi)) * Gamma[n/2-I] * Gamma[n/2+I] / Pi,{n,0,20}]] (* _Vaclav Kotesovec_, Nov 06 2014 *) %o A166741 (PARI) for (n=0,25,print(polcoeff(exp(2*asin(x)),n)*n!,",")) %Y A166741 Cf. A006228, A039661, A166748. %K A166741 nonn %O A166741 0,2 %A A166741 _Jaume Oliver Lafont_, Oct 21 2009