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 A123221 Irregular triangle read by rows: the n-th row consists of the coefficients in the expansion of Sum_{j=0..n*(n+1)/2} A008302(n+1,j)*x^j*(1 - x)^(n - min(n, j)), where A008302 is the triangle of Mahonian numbers. 12
 1, 1, 1, 0, 1, 1, 1, 0, 2, 3, 5, 3, 1, 1, 0, 3, 5, 11, 22, 20, 15, 9, 4, 1, 1, 0, 4, 7, 18, 41, 90, 101, 101, 90, 71, 49, 29, 14, 5, 1, 1, 0, 5, 9, 26, 64, 154, 359, 455, 531, 573, 573, 531, 455, 359, 259, 169, 98, 49, 20, 6, 1, 1, 0, 6, 11, 35, 91, 234, 583 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS Wikipedia, Major index FORMULA T(n,k) = A008302(n+1,k) for n + 1 <= k <= n*(n + 1)/2, n > 1. - Franck Maminirina Ramaharo, Oct 14 2018 EXAMPLE Triangle begins:     1;     1;     1, 0, 1, 1;     1, 0, 2, 3,  5,  3,  1;     1, 0, 3, 5, 11, 22, 20,  15,   9,  4,  1;     1, 0, 4, 7, 18, 41, 90, 101, 101, 90, 71, 49, 29, 14, 5, 1;     ... MATHEMATICA M[n_] := CoefficientList[Expand@Product[Sum[x^i, {i, 0, j}], {j, n - 1}], x]; Table[CoefficientList[Sum[M[n + 1][[m + 1]]*x^m*(1 - x)^(n - Min[n, m]), {m, 0, Length[M[n + 1]] - 1}], x], {n, 0, 10}]//Flatten PROG (Maxima) A008302(n, k) := ratcoef(ratsimp(product((1 - x^j)/(1 - x), j, 1, n)), x, k)\$ P(x, n) := sum(A008302(n + 1, j)*x^j*(1 - x)^(n - min(n, j)), j, 0, n*(n + 1)/2)\$ create_list(ratcoef(expand(P(x, n)), x, k), n, 0, 10, k, 0, hipow(P(x, n), x)); /* Franck Maminirina Ramaharo, Oct 14 2018 */ CROSSREFS Cf. A122753, A123018, A123019, A123021, A123027, A123199, A123202, A123202, A123217. Sequence in context: A069110 A238684 A202694 * A197032 A321781 A254862 Adjacent sequences:  A123218 A123219 A123220 * A123222 A123223 A123224 KEYWORD nonn,tabf AUTHOR Roger L. Bagula, Oct 05 2006 EXTENSIONS Edited, new name, and offset corrected by Franck Maminirina Ramaharo, Oct 14 2018 STATUS approved

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Last modified May 31 09:30 EDT 2020. Contains 334748 sequences. (Running on oeis4.)