To illustrate, in the discrete time version of (22) (see Kemeny-Snell
[35] page 212)
there is another term which must be subtracted due to
double counting on the diagonal in (17):
For T a Markov killing time of the discrete time
Markov chain, 
,
where 
is the discrete time potential kernel
for 
as in (2).
Because of diagonal terms like 
above,
the discrete time moment
formulae do not iterate neatly except
when v is the indicator of some subset B of E.
In this case 
(say) is the number of hits on B before time T,
and there is the following analog of Kac's formula for
the rising factorial moments of 
[50, 51]:
where 
is the operator of multiplication by the indicator of B.
See
[50, 51]
and Section 3.2 of [29] for further moment
formulae in discrete time.