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 A137347 Triangular sequence from coefficients of a polynomial recursion: p(x, n] = x*p(x, n - 1) - 2*x^2*p(x, n - 2) + x^3*p(x, n - 3). 0
 1, -1, 1, 0, -1, -1, 0, 0, 1, -2, 0, 0, 0, 2, 1, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 7, -3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS Row sums are: {1, 0, -2, -1, 3, 3, -4, -7, 4, 14, -1, -25, -9, 40, 33, -56} LINKS FORMULA p(x, n] = x*p(x, n - 1) - 2*x^2*p(x, n - 2) + x^3*p(x, n - 3). EXAMPLE {1}, {-1, 1}, {0, -1, -1}, {0, 0, 1, -2}, {0, 0, 0, 2, 1}, {0, 0, 0, 0, -1, 4}, {0, 0, 0, 0, 0, -4}, {0, 0, 0, 0, 0, 0, 0, -7}, {0, 0, 0, 0, 0, 0, 0, 7, -3}, {0, 0, 0, 0, 0, 0, 0, 0, 3, 11}, {0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 10}, {0, 0, 0, 0, 0,0, 0, 0, 0, 0, -10, -15}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,15, -24}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 16}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 49}, {0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, -49, -7} MATHEMATICA Clear[p, x, a0, b0] p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = x - 1; p[x_, n_] := p[x, n] = x*p[x, n - 1] - 2*x^2*p[x, n - 2] + x^3*p[x, n - 3]; g = Table[ExpandAll[p[x, n]], {n, 0, 15}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 15}]; Flatten[a] CROSSREFS Sequence in context: A317636 A305566 A326813 * A024941 A219492 A285796 Adjacent sequences:  A137344 A137345 A137346 * A137348 A137349 A137350 KEYWORD uned,tabl,sign AUTHOR Roger L. Bagula, Apr 08 2008 STATUS approved

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)