Slow COUNT

I can see it has been discussed before, why COUNT(*) tends to be slow on
PostgreSQL compared with ex. MySQL.
As far as I understood it has something to do with missing numbering on
the rows in the indexes and that there should be plenty of reasons not
to implement that in PostgreSQL, not that I found an explanation.
However I can imagine it will have an impact on inserts.

My questions is, which statements can use to count the rows faster ?
32 secs compared to 10 ms !

Thanks,
Poul

db=# explain analyze select count(*) from my.table;
QUERY PLAN

-----------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=60008.28..60008.28 rows=1 width=0) (actual
time=32028.469..32028.474 rows=1 loops=1)
-> Seq Scan on table (cost=0.00..54962.62 rows=2018262 width=0)
(actual time=14.492..19592.014 rows=2018252 loops=1)
Total runtime: 32028.750 ms
(3 rows)

db=# explain analyze select count(*) from my.table where node =
'1234567890';

QUERY PLAN

---------------------------------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=50023.14..50023.14 rows=1 width=0) (actual
time=1790.967..1790.971 rows=1 loops=1)
-> Index Scan using idx_node_date_id on table (cost=0.00..49968.76
rows=21753 width=0) (actual time=80.218..1570.747 rows=34648 loops=1)
Index Cond: ((node)::text = '1234567890'::text)
Total runtime: 1792.084 ms
(4 rows)

mysql>select count(*) from table;
+----------+
| count(*) |
+----------+
| 2018160 |
+----------+
1 row in set (0.01 sec)

mysql>select count(*) from table where node = '1234567890';
+----------+
| count(*) |
+----------+
| 34648 |
+----------+
1 row in set (0.23 sec)