The coefficient of x⁹ in the expansion of (1 + x) (1 + x²) (1 + x³) ... (1 + x¹⁰⁰) is _______.

x⁹ can be formed in following eight ways.

i.e., ${\mathrm{x}}^9,{\mathrm{x}}^{1+8},{\mathrm{x}}^{2+7},{\mathrm{x}}^{3+6},{\mathrm{x}}^{4+5},{\mathrm{x}}^{1+2+6},{\mathrm{x}}^{1+3+5},{\mathrm{x}}^{2+3+4}$

and coefficient in each case is 1.

$\therefore$ Coefficient of x⁹ = 1 + 1 + 1 +... 8 times

                                = 8