  An expression in the form of an easily computed integral is given for the
determinant of the scalar GJMS operator on an odd--dimensional sphere.
Manipulation yields a sum formula for the logdet in terms of the logdets of the
ordinary conformal Laplacian for other dimensions. This is formalised and
expanded by an analytical treatment of the integral which produces an explicit
combinatorial expression directly in terms of the Riemann zeta function, and
$\log2$. An incidental byproduct is a (known) expression for the central
factorial coefficients in terms of higher Bernoulli numbers.
