$a=1;print$a*=$b+=1,$/for a..k
[download]

24 characters using say and an unused punctuation variable:

13:38 >perl -E "$a=1;say$a*=++$}for a..k"
1
2
6
24
120
720
5040
40320
362880
3628800
39916800

13:38 >
[download]

:-)

Athanasius <°(((>< contra mundum

Iustus alius egestas vitae, eros Piratica,

Though we may have strayed a bit from the original golf, yours can be whittled by three strokes:

> perl -E "$a=1;say$a*=++$}for a..k"
> perl -E "say$x*=$_ for++$x..11"

1
2
6
24
120
720
5040
40320
362880
3628800
39916800
[download]

also this solution works only for series of consecutive integers starting with 1


perl -E "$a=1;say$a*=++$}for @ARGV" 0 1 2 3
1
2
6
24
perl -E "$a=1;say$a*=++$}for @ARGV" 1 3
1
2
[download]



L*

There are no rules, there are no thumbs..
Reinvent the wheel, then learn The Wheel; may be one day you reinvent one of THE WHEELS.