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 A175721 Array T(n,m) read by antidiagonals: the coefficient of [x^m] of 1/(-x^n +1 -x^(1+n) +x +3*x^(2+n) -2*x^2 -x^(3+n)) in row n, column 1<=m. 1
 0, 3, -1, -3, 4, -1, 10, -6, 3, -1, -18, 14, -4, 3, -1, 42, -24, 10, -5, 3, -1, -87, 47, -19, 12, -5, 3, -1, 190, -83, 42, -22, 11, -5, 3, -1, -405, 152, -84, 45, -20, 11, -5, 3, -1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Antidiagonal sums are: 0, 2, 0, 6, -6, 25, -50, 135, -304,... For large n, the rows approach A077925. LINKS FORMULA G.f.: 1/( -x^n +1 -x^(1+n) +x +3*x^(2+n) -2*x^2 -x^(3+n) ). EXAMPLE The array starts in row n=1 with columns m>=1 as 0,3,-3,10,-18,42,-87,190,-405,873,...  A077899 -1,4,-6,14,-24,47,-83,152,-268,476,... A175722 -1,3,-4,10,-19,42,-84,174,-353,726,... -1,3,-5,12,-22,45,-87,174,-340,670,... -1,3,-5,11,-20,42,-83,169,-339,686,... -1,3,-5,11,-21,44,-86,173,-343,685,... -1,3,-5,11,-21,43,-84,170,-339,681,... -1,3,-5,11,-21,43,-85,172,-342,685,... -1,3,-5,11,-21,43,-85,171,-340,682,... -1,3,-5,11,-21,43,-85,171,-341,684,... MAPLE A175721 := proc(m, k) 1/(-x^m + 1 - x^(1 + m) + x + 3*x^(2 + m) - 2* x^2 - x^(3 + m)) ; coeftayl(%, x=0, k) ; end proc: # R. J. Mathar, Dec 22 2010 MATHEMATICA f[x_, m_] = ExpandAll[(x - x^(m + 1))*(1 - x - x^2) - (1 - 2*x + x^(m + 1))]; g[x_, n_] = ExpandAll[x^(m + 3)*f[1/x, m]]; a = Table[Table[SeriesCoefficient[       Series[1/g[x, m], {x, 0, 10}], n], {n, 0, 10}], {m, 1, 10}]; Table[Table[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 1, 10}] Flatten[%] CROSSREFS Cf. A000045, A077925 Sequence in context: A173934 A131504 A008311 * A296388 A081772 A204217 Adjacent sequences:  A175718 A175719 A175720 * A175722 A175723 A175724 KEYWORD sign,tabl AUTHOR Roger L. Bagula, Dec 04 2010 STATUS approved

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Last modified January 17 18:48 EST 2019. Contains 319251 sequences. (Running on oeis4.)