Boys and a girl partition

[Jon Wild]

On Sun, 14 May 2006, koh wrote:

>    I considered partitions of a set which has {n-1} boys and a girl.
>
>    S : 1,2,4,7,12,19,30
>
>    n=5
>    {o,o,o,o,*},{o,o,*,oo},{o,o,o,o*},{*,oo,oo},{o,oo,o*},
> {o,*,ooo},{o,o,oo*},{o*,ooo},{oo,oo*},{*,oooo},{o,ooo*},{oooo*}¡¡
>    "o" means a boy, "*" means a girl.
>
>    It doesn't seem to exist on OEIS.

It's a subsequence of the more general sequence A096443, the number of 
partitions of the nth multiset. Your sequence corresponds to the 3rd, 5th, 
8th, 13th... values of A096443. There are other subsequences in the 
handbook, for example this one which seems related to yours:

A00070 Number of partitions of n into parts but there are two kinds of 
parts of size one.

Actually scratch that, that sequence *is* yours!

--Jon