[seqfan] A possible new Keyword

Juan Arias de Reyna arias at us.es
Thu Sep 24 17:47:46 CEST 2015

Frequently we consider  sequences of  polynomials in an infinite number of 

For example the fourth polynomial in a given sequence I find is

>  - u[1]^4 + 4 u[1]^2 u[2] - 2 u[2]^2 - 4 u[1] u[3] + 4 u[4]

There is a coefficient for each partition of  n = 4. In this case each coefficient is
related to a partition of 4

4 = 1 + 1 + 1 + 1       coef  -1
  = 1 + 1 + 2           coef   4
  = 1 + 3               coef  -4
  = 2 + 2               coef  -2
  = 4                   coef   4

To include the sequence of coefficients we want to give a canonical order to
all possible partitions.
I will consider useful that all partition of the number n precede all partitions of n+1.

But how to order the partitions of a number n?
Perhaps writing the summands in increasing order and then by lexicografic order  as  I have 
written above the partitions of 4.

Maybe somebody here in OEIS has a better election. 
I will like to fix a particular order, 
then in all cases that a sequence of 
this type is included in OEIS this same order should be used.  Also a new keyword as the 
actual tabf and tabl should be added to the Keywords file, to indicate this type of sequence.

Somebody know sequences of this type already included in OEIS?
Has this problem appeared before?

Best regards, 
Juan Arias de Reyna

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