Jon A. Wellner

Values of L_n, the length of the longest increasing subsequence 
in 10^4 random permutations of {1, 2, ... , n}  for n=6x10^5.
There was 1 permutations for which L_n was 1505, 2 for which 
it was 1507, and so forth.

1     1505
2     1507
1     1508
3     1509
6     1510
8     1511
7     1512
14    1513
17    1514
28    1515
44    1516
62    1517
83    1518
100   1519
113   1520
187   1521
199   1522
218   1523
247   1524
363   1525
324   1526
393   1527
406   1528
428   1529
444   1530
470   1531
464   1532
534   1533
476   1534
459   1535
444   1536
450   1537
408   1538
395   1539
329   1540
278   1541
257   1542
249   1543
201   1544
161   1545
133   1546
120   1547
86    1548
66    1549
67    1550
57    1551
38    1552
34    1553
27    1554
18    1555
21    1556
14    1557
10    1558
6     1559
7     1560
7     1561
7     1562
2     1563
2     1564
3     1565
1     1566
1     1568