cp's OEIS Frontend

A113247 Number of permutations pi in S_n such that maj pi and maj pi^(-1) have the same parity where maj is the major index. Equivalently, the number of pi such that maj pi and inv pi have the same parity where inv is the inversion number.

%I A113247 #7 May 02 2016 10:35:44
%S A113247 1,1,2,4,16,64,384,2544,20352,181632,1816320,19960320,239523840,
%T A113247 3113533440,43589468160,653837506560,10461400104960,177843719208960,
%U A113247 3201186945761280,60822550297313280,1216451005946265600
%N A113247 Number of permutations pi in S_n such that maj pi and maj pi^(-1) have the same parity where maj is the major index. Equivalently, the number of pi such that maj pi and inv pi have the same parity where inv is the inversion number.
%C A113247 a(2n) and a(2n+1) are both divisible by 2^n n! a(2n) = 2n a(2n-1) The number of pi in S_n such that maj pi and maj pi^(-1) are both even is exactly half of a(n)
%H A113247 H. Barcelo, B. Sagan and S. Sundaram, <a href="http://www.math.msu.edu/~sagan/Papers/cpc.pdf">Counting permutations by congruence class of major index</a>, preprint, 2005.
%H A113247 H. Barcelo, B. Sagan and S. Sundaram, <a href="http://dx.doi.org/10.1016/j.aam.2006.03.002">Counting permutations by congruence class of major index</a>, Advances in Applied Mathematics, Volume 39, Issue 2, August 2007, Pages 269-281.
%F A113247 a(2n) = 2 n^2 a(2n-2) + 2 n (n-1) b(2n-2) and a(2n+1) = 2 n (n+1) a(2n-1) + 2 n^2 b(2n-1) where b(n) is sequence A113248
%e A113247 a(3)=4 because the following 4 permutations in S_3 have the same parity for their major index and the major index of their inverse (and in fact are equal to their inverse): 123, 213, 321, 132.
%Y A113247 Cf. A113248.
%K A113247 nonn
%O A113247 0,3
%A A113247 _Bruce E. Sagan_, Oct 20 2005