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%I #12 Sep 29 2012 06:26:26
%S 1,2,4,10,28,116,576,3634,26620,223440,2100964,21888712,250062982,
%T 3108430640
%N Number of permutations in S_n with major index equal to inversion number.
%C At first equal to and eventually greater than corresponding entry of A195924, number of fixed points of Foata's bijection.
%C For any large n, the two permutations with maj and inv both 2 are 2314..n, and 14235..n.
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/demo/seq/#A207018">C++ program to compute terms</a>.
%e A(4)=10: the 10 permutations of 4 elements with major index equal to inversion number are
%e #: perm #inv. inversion table
%e 1: [ 0 1 2 3 ] 0 [ 0 0 0 ]
%e 2: [ 0 3 1 2 ] 2 [ 0 2 0 ]
%e 3: [ 1 0 2 3 ] 1 [ 0 0 1 ]
%e 4: [ 1 2 0 3 ] 2 [ 0 1 1 ]
%e 5: [ 1 2 3 0 ] 3 [ 1 1 1 ]
%e 6: [ 2 1 0 3 ] 3 [ 0 1 2 ]
%e 7: [ 2 1 3 0 ] 4 [ 1 1 2 ]
%e 8: [ 2 3 1 0 ] 5 [ 1 2 2 ]
%e 9: [ 3 0 2 1 ] 4 [ 1 0 3 ]
%e 10: [ 3 2 1 0 ] 6 [ 1 2 3 ]
%Y Cf. A195924.
%K nonn,hard,more
%O 1,2
%A _William J. Keith_, Feb 14 2012
%E a(14) by _Joerg Arndt_, Sep 29 2012.
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