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 A156890 A new infinite sum polynomial coefficient triangle sequence: p(x,n)=((1 + x - x^2)^ (n + 1))*Sum[(k + 1)^n*(-x + x^2)^k, {k, 0, Infinity}]. 0
 1, 1, 1, -1, 1, 1, -4, 5, -2, 1, 1, -11, 22, -23, 14, -3, 1, 1, -26, 92, -158, 145, -82, 32, -4, 1, 1, -57, 359, -906, 1265, -1135, 649, -238, 67, -5, 1, 1, -120, 1311, -4798, 9630, -12132, 10163, -5970, 2406, -620, 135, -6, 1, 1, -247, 4540, -24205, 66769, -113626 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Row sums are all one. LINKS FORMULA p(x,n)=((1 + x - x^2)^ (n + 1))*Sum[(k + 1)^n*(-x + x^2)^k, {k, 0, Infinity}]; t(n,m)=coefficiuents(p(x,n)). EXAMPLE {1}, {1}, {1, -1, 1}, {1, -4, 5, -2, 1}, {1, -11, 22, -23, 14, -3, 1}, {1, -26, 92, -158, 145, -82, 32, -4, 1}, {1, -57, 359, -906, 1265, -1135, 649, -238, 67, -5, 1}, {1, -120, 1311, -4798, 9630, -12132, 10163, -5970, 2406, -620, 135, -6, 1}, {1, -247, 4540, -24205, 66769, -113626, 131045, -106889, 62261, -26426, 8033, -1517, 268, -7, 1}, {1, -502, 15110, -117450, 435500, -977696, 1481152, -1595250, 1261165, -743880, 324952, -105274, 25220, -3570, 530, -8, 1}, {1, -1013, 48853, -550872, 2723770, -7917346, 15324278, -21123948, 21577667, -16668355, 9841007, -4462316, 1530826, -391734, 76330, -8188, 1049, -9, 1} MATHEMATICA Clear[p, x, n, m]; p[x_, n_] = ((1 + x - x^2)^ (n + 1))*Sum[(k + 1)^n*(-x + x^2)^k, {k, 0, Infinity}]; Table[Expand[FullSimplify[ExpandAll[p[x, n]]]], {n, 0, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A157784 A274615 A258895 * A320480 A163531 A267095 Adjacent sequences:  A156887 A156888 A156889 * A156891 A156892 A156893 KEYWORD tabl,uned,sign AUTHOR Roger L. Bagula, Feb 17 2009 STATUS approved

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Last modified January 21 19:08 EST 2019. Contains 319350 sequences. (Running on oeis4.)