I need a hint

[wouter meeussen]

can anybody help me further with this?

define function 'runs' as
runs[li : {__Integer}] := ((Length /@ Split[#])) &  [Sort at li]

saying :  count the runs of equal integers in a sorted list,
runs[ {1,1,1,3,3,7}]  gives {3,2,1},

next define 'multiplicity' as the multinomial of the runs,
multiplicity[{1,1,1,3,3,7}] gives 6!/(3!*2!*1!) = 60

Given all that, can anyone make this poor soul understand why
the sum of the multiplicities of the partitions of n equals 2^(n-1) ?

blushingly yours,

Wouter.