-------------------------------------------------------------------- Actual subject: On the true nature of A215940 --------------------------------------------------------------------
Upon the interesting Diophantine F(k)=−1*k^2 + 20*k
recreating such sequence, these numbers are the coefficients for the polynomial g(r) in r=20 that gives the last one inside the first 20! terms of A215940.
g(r)= sum_{u=1..r} F(u-1)*r^(r-u)
g(20)= 5488245866744423385333139.
What is interesting here is not big quotient described by g(20), but the following (observed) fact:
There exists <--- for the last element inside each set with the first N! terms of A215940 ---> a symmetric set of coefficients for the polynomial
that describes it in a base independent way.
This behavior suggest additionally to treat the quotients defined in A215940 as vectors in the sense of the Tensor Algebra and Calculus used in Physics ( I mean base independent for the present context if it where allowed the
analogy between the radices for the positional systems and the coordinate systems ).
Therefore it must be definable a sort of vector space equipped with the permutations without repetitions as its elements and a proper definition
of inner product which yields the quotients A215940 explaining why they are invariant.
A215940 actually is a tensor problem.
Cheers.
R. J. Cano
P.S.: These are the first 20 sets where it have sense to define them.
This is the true kind of "Universally invariant" look of the terms (*) for A215940!!
First consequence. Property: The greatest coefficient in each one of those sets is the smallest radix from which all the terms looks unchanged under radix conversion, referring here to the first (m+1)! terms of A215940 where m is the first coefficient from left to right
in the corresponding row.
--------- (*) f.n.: Placed at exact factorial offsets.