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a(n) = maximal value of C(i, j) * C(n-j, n-i) for 0 <= j <= i <= n.
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%I #5 Aug 23 2013 09:54:34

%S 1,2,4,9,18,40,100,225,525,1225,3136,7056,17640,44100,108900,261360,

%T 637065,1656369,4008004,10020010,25050025,64128064,155739584,

%U 393853824,1012766976,2538950544,6347376360,15868440900,41408180100,102252852900

%N a(n) = maximal value of C(i, j) * C(n-j, n-i) for 0 <= j <= i <= n.

%C This is the number of longest common subsequences between two binary strings of the form 00...011...1.

%C This is a lower bound for A094837, equivalent to choosing first string (x "a"s followed by (n-x) "b"s) and second string (y "a"s followed by (n-y) "b"s).

%e a(3) is maximal with x=1, y=2, giving a(3) = C(2,1) * C(3-1,3-2). This is equivalent to the number of instances of length-2 common subsequences between "aab" and "abb".

%Y Cf. A094858-A094862, A094837, A094824, A094349, A094350.

%K nonn

%O 1,2

%A _Hugo van der Sanden_, Jun 15 2004