Clean cumulative sum alongside grouped sum - psql

Question

I am working in PostgreSQL 9.6.6
For the sake of reproducibility, I'll use create tempory table to create a "constant" table to play with:
create temporary table test_table as
select * from
(values
('2018-01-01', 2),
('2018-01-01', 3),
('2018-02-01', 1),
('2018-02-01', 2))
as t (month, count)
A select * from test_table returns the following:
month | count
------------+-------
2018-01-01 | 2
2018-01-01 | 3
2018-02-01 | 1
2018-02-01 | 2
The desired output is the following:
month | sum | cumulative_sum
------------+-----+----------------
2018-01-01 | 5 | 5
2018-02-01 | 3 | 8
In other words, the values have been summed, grouping by month, and then the cumulative sum is displayed in another column.
The issue is that the only way I know to achieve this is somewhat convoluted. The grouped sum must be computed first, (as with a sub select or with statement), and then the running tally is computed with a select statement against that table, as so:
with sums as
(select month,
sum(count) as sum
from test_table
group by 1)
select month,
sum,
sum(sum) over (order by month) as cumulative_sum
from sums
What I wish could work would be something more like...
select month,
sum(count) as sum,
sum(count) over (order by month) as cumulative_sum
from test_table
group by 1
But this returns
ERROR: column "test_table.count" must appear in the GROUP BY clause or be used in an aggregate function
LINE 3: sum(count) over (order by month) as cumulative_sum
No amount of fussing with the group by clause seems to satisfy PSQL.
TL,DR: is there a way in PSQL to compute both a sum over groups and the cumulative sum over groups using just a single select statement? More generally, is there a "preferred" way to accomplish this, beyond the method I use in this question?

Answer 1

Your hunch to use SUM as an analytic function was on the right track, but you need to analytic sum the aggregate sum:
SELECT month,
SUM(count) as sum,
SUM(SUM(count)) OVER (ORDER BY month) AS cumulative_sum
FROM test_table
GROUP BY 1;
Demo
As to why this works, the analytic functions are applied after the GROUP BY clause has happened. So the aggregate sum in fact is available when we go take the rolling sum.