Before revision:  In particular, we obtain an explicit binomial identity for the sums of elements lying on the diagonals kx+my=n in Pascal's triangle \mathbb N_0\times \mathbb N_0\ni(x,y)\mapsto {x+y\choose x} . This provides a missing piece in the earlier work of Dickinson ~\mbox{%DIFAUXCMD Dickinson19500pt%DIFAUXCMD , Raab \mbox{%DIFAUXCMD Raab1963}0pt%DIFAUXCMD }  ]  , and Green \mbox{%DIFAUXCMD Green1968 .
After revision:  In particular, we obtain an explicit binomial identity for the sums of elements lying on the diagonals kx+my=n in Pascal's triangle \mathbb N_0\times \mathbb N_0\ni(x,y)\mapsto {x+y\choose x} 0pt%DIFAUXCMD , Raab \mbox{%DIFAUXCMD Raab1963}0pt%DIFAUXCMD } ] , and Green \mbox{%DIFAUXCMD Green1968 .