A207018 Number of permutations in S_n with major index equal to inversion number.

1, 2, 4, 10, 28, 116, 576, 3634, 26620, 223440, 2100964, 21888712, 250062982, 3108430640

Offset

1,2

Comments

At first equal to and eventually greater than corresponding entry of A195924, number of fixed points of Foata's bijection.

For any large n, the two permutations with maj and inv both 2 are 2314..n, and 14235..n.

Links

Table of n, a(n) for n=1..14.

Joerg Arndt, C++ program to compute terms.

Example

A(4)=10: the 10 permutations of 4 elements with major index equal to inversion number are
   #:       perm      #inv.   inversion table
   1:    [ 0 1 2 3 ]   0    [ 0 0 0 ]
   2:    [ 0 3 1 2 ]   2    [ 0 2 0 ]
   3:    [ 1 0 2 3 ]   1    [ 0 0 1 ]
   4:    [ 1 2 0 3 ]   2    [ 0 1 1 ]
   5:    [ 1 2 3 0 ]   3    [ 1 1 1 ]
   6:    [ 2 1 0 3 ]   3    [ 0 1 2 ]
   7:    [ 2 1 3 0 ]   4    [ 1 1 2 ]
   8:    [ 2 3 1 0 ]   5    [ 1 2 2 ]
   9:    [ 3 0 2 1 ]   4    [ 1 0 3 ]
  10:    [ 3 2 1 0 ]   6    [ 1 2 3 ]

Crossrefs

Cf. A195924.

Sequence in context: A022492 A352068 A123429 * A006841 A003223 A061417

Adjacent sequences: A207015 A207016 A207017 * A207019 A207020 A207021

Keyword

nonn,hard,more

Author

William J. Keith, Feb 14 2012

Extensions

a(14) by Joerg Arndt, Sep 29 2012.

Status

approved