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We show that the Hilbert series of the projective variety $X=P(O_{min}),$corresponding to the minimal nilpotent orbit $\mathcal O_{min},$ is universalin the sense of Vogel: it is written uniformly for all simple Lie algebras interms of Vogel's parameters $\alpha,\beta,\gamma$ and represents a special caseof the generalized hypergeometric function ${}_{4}F_{3}.$ A universal formulafor the degree of $X$ is then deduced.

Universal formula for Hilbert series of minimal nilpotent orbits