A080169

[Jens Voss]

The definition of the new sequence A080169 reads:

> ID Number: A080169
> Sequence:  1,3,13,81,541
> Name:      Ways n competitors can rank in a competition, allowing for the
>               possibility of ties.
> Example:   Three competitors can finish in 13 ways: 1,2,3; 1,3,2; 2,1,3; 2,3,1;
>               3,1,2; 3,2,1; 1,1,3; 2,2,1; 1,3,1; 2,1,2; 3,1,1; 1,2,2; 1,1,1.
> Keywords:  more,nonn,new
> Offset:    1
> Author(s): Robert Lozyniak (nothing at example.com), Feb 04 2003

Either I misunderstood this, or I can't count or there's a mistake:
I am getting only 75 for a(4):

 The  1 way of all four coming in first,
 the  8 ways of having three come in simultaneously and one separately,
 the  6 ways of having two pairs,
 the 36 ways of having one pair and two separate competitors as well as
 the 24 ways of all four coming in separately
-------
sum: 75

Which ones did I miss?

Regards,
Jens