A249074 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
1, 4, 1, 6, 4, 1, 32, 14, 4, 1, 60, 72, 24, 4, 1, 384, 228, 120, 36, 4, 1, 840, 1392, 564, 176, 50, 4, 1, 6144, 4488, 3312, 1140, 240, 66, 4, 1, 15120, 31200, 14640, 6480, 2040, 312, 84, 4, 1, 122880, 104880, 97440, 37440, 11280, 3360, 392, 104, 4, 1, 332640
Offset: 0
Examples
f(0,x) = 1/1, so that p(0,x) = 1; f(1,x) = (4 + x)/1, so that p(1,x) = 4 + x; f(2,x) = (6 + 4*x + x^2)/(4 + x), so that p(2,x) = 6 + 4*x + x^2. First 6 rows of the triangle of coefficients: 1 4 1 6 4 1 32 14 4 1 60 72 24 4 1 384 228 120 36 4 1
Links
- Clark Kimberling, Rows 0..100, flattened
Programs
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Mathematica
z = 11; p[x_, n_] := x + 2 n/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}]] (* A249074 array *) Flatten[CoefficientList[u, x]] (* A249074 sequence *) v = u /. x -> 1 (* A249075 *) u /. x -> 0 (* A087299 *)
Comments