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A060701 Table by antidiagonals of Mahonian numbers T(n,k): permutations of n letters with k inversions.

%I A060701 #7 May 04 2013 18:28:49
%S A060701 1,0,1,0,1,1,0,0,2,1,0,0,2,3,1,0,0,1,5,4,1,0,0,0,6,9,5,1,0,0,0,5,15,
%T A060701 14,6,1,0,0,0,3,20,29,20,7,1,0,0,0,1,22,49,49,27,8,1,0,0,0,0,20,71,98,
%U A060701 76,35,9,1,0,0,0,0,15,90,169,174,111,44,10,1,0,0,0,0,9,101,259,343,285
%N A060701 Table by antidiagonals of Mahonian numbers T(n,k): permutations of n letters with k inversions.
%D A060701 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, 1999; see Corollary 1.3.10, p. 21.
%F A060701 T(n, k)=sum_{j=0..n}[T(n-1, k-j)].
%F A060701 Product (1+x+...+x^k), k=1..n-1 = Sum T(n, k)x^k, k=0..n(n-1)/2.
%e A060701 1;
%e A060701 0,1;
%e A060701 0,1,1;
%e A060701 0,0,2,1;
%e A060701 0,0,2,3,1;
%e A060701 0,0,1,5,4,1;
%e A060701 0,0,0,6,9,5,1; ...
%e A060701 [1, 4, 2, 3], [1, 3, 4, 2], [2, 1, 4, 3], [2, 3, 1, 4], [3, 1, 2, 4] have 2 inversions so T(4, 2)=5.
%o A060701 (PARI) T(n,k)=polcoeff(prod(j=1,n-1,sum(i=0,j,x^i)),k)
%Y A060701 A008302 is the main entry for these numbers. Columns include A000012, A000027, A000096, A005286, A005287, A005288. Diagonals include A000707, A001892, A001893, A001894, A005283, A005284, A005285.
%K A060701 nonn,tabl
%O A060701 0,9
%A A060701 _Henry Bottomley_, Apr 25 2001
%E A060701 Additional comments from _Michael Somos_, Jun 23 2002.