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 A203300 Self-generating triangle based on symmetric functions. 2
 1, 1, 1, 1, 2, 1, 1, 4, 5, 2, 1, 12, 49, 78, 40, 1, 180, 11085, 270610, 2094264, 1834560, 1, 4210700, 4952544856489, 1094968722994345590, 11723079808649412379800, 2086231309557403469400000, 2074509324712524510720000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Let row n+1 be (c0, c1, c2,...,cn).  Then c0*x^n + c1*x^(n-1) +...+ cn=(x+b0)(x+b1)...(x+bm), where (b0,b1,b2,...,bm) is row n. LINKS FORMULA row n+1: f(0,r), f(1,r),...f(n,r), where f(k,r)=(k-th elementary symmetric function), r=(row n). EXAMPLE First five rows: 1 1...1 1...2....1 1...4....5....2 1...12...49...78...40 The factorization property is illustrated by x^2 + 2x + 1 -> (x+1)(x+2)(x+1) = x^3 + 4x^2 + 5x + 2. MATHEMATICA s =.; s[1] = {1}; Prepend[Table[s[z] = Table[SymmetricPolynomial [k, s[z - 1]], {k, 0, z - 1}], {z, 2, 7}], s[1]] % // TableForm (* A203300 triangle *) %% // Flatten  (* A203300 sequence *) (* Peter J. C. Moses, Dec 30 2011 *) CROSSREFS Cf. A203301. Sequence in context: A198895 A118686 A102610 * A134172 A208061 A078047 Adjacent sequences:  A203297 A203298 A203299 * A203301 A203302 A203303 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 31 2011 STATUS approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)