Values of L_n, the length of the longest increasing subsequences in 
10^5 random permutations on {1, 2, ..., n} for n = 10^6.  There was 
1 permutation in which L_n was 1948, 1 in which it was 1949, 3 in 
which it was 1952, and so on.

   1 1948
   1 1949
   3 1952
   5 1953
   4 1954
  13 1955
  18 1956
  42 1957
  53 1958
  91 1959
 111 1960
 155 1961
 221 1962
 310 1963
 421 1964
 557 1965
 699 1966
 862 1967
1137 1968
1417 1969
1689 1970
1999 1971
2277 1972
2661 1973
2978 1974
3241 1975
3557 1976
3849 1977
4118 1978
4226 1979
4444 1980
4472 1981
4431 1982
4561 1983
4538 1984
4209 1985
4002 1986
3809 1987
3548 1988
3242 1989
2938 1990
2658 1991
2425 1992
2145 1993
1941 1994
1667 1995
1396 1996
1205 1997
1005 1998
 905 1999
 723 2000
 597 2001
 513 2002
 393 2003
 322 2004
 254 2005
 206 2006
 164 2007
 134 2008
  98 2009
  85 2010
  57 2011
  45 2012
  34 2013
  34 2014
  27 2015
  10 2016
  20 2017
   2 2018
   6 2019
   4 2020
   2 2021
   3 2022
   1 2023
   2 2024
   1 2025
   5 2026
   1 2027