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 A249139 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments. 1
 1, 3, 1, 5, 2, 11, 7, 1, 21, 16, 3, 43, 41, 12, 1, 85, 94, 34, 4, 171, 219, 99, 18, 1, 341, 492, 261, 60, 5, 683, 1101, 678, 195, 25, 1, 1365, 2426, 1692, 576, 95, 6, 2731, 5311, 4149, 1644, 340, 33, 1, 5461, 11528, 9959, 4488, 1106, 140, 7, 10923, 24881 (list; 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) = 1 + (x + 2)/f(n-1,x), where f(0,x) = 1. (Sum of numbers in row n) = A006130(n+1) for n >= 0. (Column 1) is essentially A001045. 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 + 2 x)/(3 + x), so that p(2,x) = 5 + 2 x. First 6 rows of the triangle of coefficients: 1 3    1 5    2 11   7    1 21   16   3 43   41   12  1 MATHEMATICA z = 15; f[x_, n_] := 1 + (x + 2)/f[x, n - 1]; f[x_, 1] = 1; t = Table[Factor[f[x, n]], {n, 1, z}] u = Numerator[t] TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249139 array *) Flatten[CoefficientList[u, x]] (* A249139 sequence *) CROSSREFS Cf. A006130, A001045. Sequence in context: A065168 A318581 A065277 * A059971 A184343 A099548 Adjacent sequences:  A249136 A249137 A249138 * A249140 A249141 A249142 KEYWORD nonn,tabf,easy AUTHOR Clark Kimberling, Oct 23 2014 STATUS approved

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Last modified March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)