# [seqfan] Re: number of different digit patterns of n-digit numbers

franktaw at netscape.net franktaw at netscape.net
Fri Aug 28 00:44:39 CEST 2009

```This is just the number of set partitions of n into at most 10 parts.
The condition that the first ball not go in the first box is not
relevant; you can always permute the digits so that the first one is
not zero.

Sequences of this type are in the OEIS for up to 8 (i.e., set
partitions into at most 8 parts, which is A099263).

Here's a PARI program to generate sequences of this type:

a(n,k)=local(ps);ps=exp(sum(i=1,k,x^i/i!)+x*O(x^n));vector(n,i,polcoeff(p
s,i)*i!)

Here n is the number of terms you want, and k is the maximum number of
parts.  For k = 10, we get:

1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678569, 4213584,
27644267, 190897305, 1382935569, 10479884654, 82861996310,
682044632178, 5832378929502, 51720008131148, 474821737584174,
4506150050048604, 44145239041717738, 445876518513670356,
4637570299337888742, 49618383871367215282, 545551902886241817684,
6158380541703927984540, 71311068810038965177080,
846359710104516310431744

-----Original Message-----
From: Tanya Khovanova <mathoflove-seqfan at yahoo.com>

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

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```