[seqfan] Even or odd, true or false?

[Peter Luschny]

Hi,

let for n, k >= 0
      A(n, k) = Hypergeometric2F1([-k, k + 1], [-k - 1], n).

Conjecture: A(n, k) is odd if and only if n is even or
(n is odd and k + 2 = 2^j for some j > 0).

Peter