sql syntax - use rollup ? - avg of count(1)

I start with something like -

select fk_column, count(1) from atable
group by fk_column.

I get a bunch of columns and their counts..

What I want is the average of all of them *without using report functionality* like compute avg of x on ..

So, I can do it with a subquery like

select avg(a) from
(select fk_column, count(1) a from
a table group by fk_column)

but can I do it with some variation of rollup?

select fk_column, avg(count(1)) as anaverage from sometable group by rollup (fk_column);

does not work..

any ideas? Heading down wrong path?

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