querying multidimensional sequences in OEIS

[franktaw at netscape.net]

I don't know of any standard for functions of an arbitrary finite 
sequence
of positive integers in the OEIS.

In your example, the function is commutative, which makes it 
essentially
a function of the multiset of values - or in other words, of a 
partition.  For
that there is a standard - two of them actually.  One is the 
enumeration
in Abramowitz and Stegun order, as specified in A036036, and the other
is the Mathematica ordering, as specified in A080577.

There are some relevant sequences in the database in both orders, some
only in the A&S order, and a few only in the Mma order.

Since the two orders are the same for partitions of up to 5 objects, 
one
often just search for an early part of the sequence.  If this does not 
suffice,
one should try both before giving up.

For example, the partitions of 5 objects are: [5], [4,1], [3,2], 
[3,1^2],
[2^2,1], [2,1^3], [1^5].  The multinomial coefficients for these are:

1,5,10,20,30,60,120

A search for this turns up A036038, the A&S version, and A078760, the
Mma version.

----
As for arbitrary finite sequences of positive integers, there are two 
main
candidates for an ordering: A066099 and A108244; these are the reverse
of each other.  I would probably go with A066099, as it is closest to 
the
ordering used for the partitions; but you can make an argument for 
either
one.  Possibly both should be used.

Off hand, I can't think of any interesting functions of finite 
sequences of
positive integers that depend on the order of the sequence.

Franklin T. Adams-Watters


-----Original Message-----
From: maxale at gmail.com

I have a sequence indexed by vectors with non-negative integer 
components. 
Is there a regular way to query such sequence in OEIS ? 
 
As an example, let us consider a sequence of multinomial coefficients. 
Any vector with non-negative integer components [k1, k2, ..., kn] 
defines an element of this sequence: 
 
a( [k1, k2, ..., kn] ) = (k1 + k2 + ... + kn)! / (k1! * k2! * ... * 
kn!) 
 
Assume that I know nothing about these numbers and have only a 
black-box computing a(v) for any given vector v with non-negative 
integer components. Can I anyhow find this sequence in OEIS and learn 
that its elements called "multinomial coefficients" ? 
 
Thanks, 
Max 


________________________________________________________________________
Check Out the new free AIM(R) Mail -- 2 GB of storage and 
industry-leading spam and email virus protection.