Determinant of the all-ones matrix with zeros on the diagonal after the first entry

Calculate det A, if

\[ A = \left[ { \begin{array} { l l l l l } { 1 } & { 1 } & { 1 } & { \dots } & { 1 } \\ { 1 } & { 0 } & { 1 } & { \dots } & { 1 } \\ { 1 } & { 1 } & { 0 } & { \dots } & { 1 } \\ { \vdots } & { \vdots } & { \vdots } & { \ddots } & { \vdots } \\ { 1 } & { 1 } & { 1 } & { \dots } & { 0 } \end{array} } \right] .\tag{2} \]