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 A162445 #6 Jul 22 2025 06:55:07
%S A162445 1,8,384,46080,2064384,3715891200,392398110720,1428329123020800,
%T A162445 274239191619993600,1678343852714360832000,102043306245033138585600,
%U A162445 4714400748520531002654720000,160144566965128191597871104000
%N A162445 A sequence related to the Beta function.
%C A162445 We define F(z) = Beta(1/2-z/2,1/2+z/2)/Beta(1/2,1/2) = 1/sin(Pi*(1+z)/2) with Beta(z,w) the Beta function. See A008956 for a closely related function.
%C A162445 For the Taylor series expansion of F(z) we can write F(z) = sum(b(n)*(Pi*z)^(2*n)/a(n), n=0..infinity) with b(n) = A046976(n) and a(n) the sequence given above.
%C A162445 We can also write F(z) = sum(c(n)*(Pi*z)^(2*n)/d(n), n=0..infinity) with c(n) = A000364(n) and d(n) = A067624(n).
%C A162445 If p(n) is the exponent of the prime factor 2 in a(n) than p(n) = A120738(n) and 2^p(n) = A061549(n) = abs((4*n)!!/A117972(n)).
%F A162445 a(n) = denom(euler(2*n)/(4*n)!!)
%t A162445 Denominator[Table[EulerE[2n]/(4n)!!,{n,0,20}]] (* _Harvey P. Dale_, Jun 23 2013 *)
%Y A162445 Bisection of A050971
%Y A162445 Equals 2^(2*n)*A046977(n)
%Y A162445 Cf. A008956, A046976, A000364, A067624, A120738, A061549 and A117972.
%K A162445 easy,frac,nonn
%O A162445 0,2
%A A162445 _Johannes W. Meijer_, Jul 06 2009