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 A060701 Table by antidiagonals of Mahonian numbers T(n,k): permutations of n letters with k inversions. 2
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 REFERENCES R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, 1999; see Corollary 1.3.10, p. 21. LINKS FORMULA T(n, k)=sum_{j=0..n}[T(n-1, k-j)]. Product (1+x+...+x^k), k=1..n-1 = Sum T(n, k)x^k, k=0..n(n-1)/2. EXAMPLE 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; ... [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. PROG (PARI) T(n, k)=polcoeff(prod(j=1, n-1, sum(i=0, j, x^i)), k) CROSSREFS 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. Sequence in context: A122851 A064301 A199881 * A275345 A259668 A261118 Adjacent sequences:  A060698 A060699 A060700 * A060702 A060703 A060704 KEYWORD nonn,tabl AUTHOR Henry Bottomley, Apr 25 2001 EXTENSIONS Additional comments from Michael Somos, Jun 23 2002. STATUS approved

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Last modified August 14 19:09 EDT 2020. Contains 336483 sequences. (Running on oeis4.)