0,2

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.

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.

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).

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)).

a(n) = denom(euler(2*n)/(4*n)!!)

Bisection of A050971

Equals 2^(2*n)*A046977(n)

Cf. A008956, A046976, A000364, A067624, A120738, A061549 and A117972.

Sequence in context: A072447 A151932 A096205 this_sequence A067624 A096204 A153836

Adjacent sequences: A162442 A162443 A162444 this_sequence A162446 A162447 A162448

easy,frac,nonn

Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009