[seqfan] number of different digit patterns of n-digit numbers

[Tanya Khovanova]

Dear Sequence Fans,

I would like to propose a new sequence:

Number of different digit patterns of n-digit numbers.
or
Number of ways to put n labeled balls into 10 indistinguishable boxes so that the first ball can't go into the first box.
or 
Number of equivalence classes of n-digit numbers with respect to digit permutations.

The sequence starts at Bell numbers: 1,2,5,15,52,203,877,4140,21147, but are not Bell numbers.

I know that OEIS is on vacation, but I need this sequence for my blog essay. So I am not sure if I should submit.

Besides, I need more terms to distinguish it from Bell numbers.

What should I do, and can you help?

Tanya