OFFSET
0,2
COMMENTS
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.
FORMULA
a(n) = denom(euler(2*n)/(4*n)!!)
MATHEMATICA
Denominator[Table[EulerE[2n]/(4n)!!, {n, 0, 20}]] (* Harvey P. Dale, Jun 23 2013 *)
CROSSREFS
KEYWORD
easy,frac,nonn
AUTHOR
Johannes W. Meijer, Jul 06 2009
STATUS
approved