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 A249100 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments. 2
 1, 3, 1, 5, 3, 1, 21, 12, 3, 1, 45, 48, 21, 3, 1, 231, 177, 81, 32, 3, 1, 585, 855, 450, 120, 45, 3, 1, 3465, 3240, 2070, 930, 165, 60, 3, 1, 9945, 18000, 10890, 4110, 1695, 216, 77, 3, 1, 65835, 71505, 57330, 28560, 7245, 2835, 273, 96, 3, 1, 208845, 443835 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + (2*n - 1)/f(n-1,x), where f(0,x) = 1.  (Sum of numbers in row n) = A249101(n) for n >= 0.  (n-th term of column 1) = A235136(n) for n >= 1. LINKS Clark Kimberling, Rows 0..100, flattened EXAMPLE f(0,x) = 1/1, so that p(0,x) = 1 f(1,x) = (3 + x)/1, so that p(1,x) = 3 + x; f(2,x) = (5 + 3 x +  x^2)/(3 + x), so that p(2,x) = 5 + 3 x +  x^2). First 6 rows of the triangle of coefficients: 1 3    1 5    3    1 21   12   3    1 45   48   21   3    1 231  177  81   32   3   1 MATHEMATICA z = 11; p[x_, n_] := x + (2 n - 1)/p[x, n - 1]; p[x_, 1] = 1; t = Table[Factor[p[x, n]], {n, 1, z}] u = Numerator[t] TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249100 array *) Flatten[CoefficientList[u, x]] (* A249100 sequence  *) v = u /. x -> 1  (* A249101 *) u /. x -> 0  (* A235136 *) CROSSREFS Cf. A249101, A245136, A087299. Sequence in context: A135224 A209578 A268829 * A152203 A161946 A013597 Adjacent sequences:  A249097 A249098 A249099 * A249101 A249102 A249103 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Oct 21 2014 STATUS approved

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Last modified November 17 22:58 EST 2018. Contains 317279 sequences. (Running on oeis4.)