A006522 is the partial sum of A004006

[Jonathan Post]

Again, because of njas' summer vacation, I am not submitting these
through the OEIS form for comments or to add cross-refs.

A004006  C(n,1)+C(n,2)+C(n,3), or n*(n^2+5)/6.

A006522  4-dimensional analogue of centered polygonal numbers. Also
number of regions created by sides and diagonals of n-gon.
(n-1)*(n-2)*(n^2-3*n+12)/24.

An interesting survey by Laurent Saloff-Coste discusses cut-off
phenomena with many examples:

http://www.math.cornell.edu/~lsc/chap5.pdf

(the published version is "Random walks on finite groups" in
Probability on discrete structures, 263–346, Encyclopaedia Math. Sci.,
110, Springer, 2004).

Perhaps that should be added to the references for A004006, because
A004006 comes up in "Burnside group B(3,n) has order 3^a(n)" and the
Burnside groups are used in the Laurent Saloff-Coste paper on random
walks in groups, as they relate to remarkable results in shuffles.

-- Jonathan Vos Post