Not that anyone who reads this would care,

[sombragris]

but I just stumbled upon another nifty property:

In the expansion of (x1 + x2 + x3 + x4 + ... + xi)n

the coefficient of the term with (x1a1)(x2a2) ... (xiai)

equals n!/((a1!)(a2!)...(an!))

(thanks,
meritite :D)