Soichi Okada and Christian Krattenthaler
\def\flp#1{\lfloor#1\rfloor} \def\clp#1{\lceil#1\rceil}
We compute the number of all rhombus tilings of a hexagon with sides $a,b+1,c,a+1,b,c+1$, of which the central triangle is removed, provided $a,b,c$ have the same parity. The result is $B(\clp{\frac {a} {2}},\clp{\frac {b} {2}},\clp{\frac {c} {2}}) B(\clp{\frac {a+1} {2}},\flp{\frac {b} {2}},\clp{\frac {c} {2}}) B(\clp{\frac {a} {2}},\clp{\frac {b+1} {2}},\flp{\frac {c} {2}}) B(\flp{\frac {a} {2}},\clp{\frac {b} {2}},\clp{\frac {c+1} {2}})$, where $B(\alpha,\beta,\gamma)$ is the number of plane partitions inside the $\alpha\times \beta\times \gamma$ box. The proof uses nonintersecting lattice paths and a new identity for Schur functions, which is proved by means of the minor summation formula of Ishikawa and Wakayama. A symmetric generalization of this identity is stated as a conjecture.