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A249251
Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
3
1, 1, 3, 1, 6, 6, 1, 9, 21, 12, 1, 12, 45, 60, 24, 1, 15, 78, 171, 156, 48, 1, 18, 120, 372, 558, 384, 96, 1, 21, 171, 690, 1473, 1656, 912, 192, 1, 24, 231, 1152, 3225, 5160, 4608, 2112, 384, 1, 27, 300, 1785, 6219, 13083, 16584, 12240, 4800, 768, 1, 30
OFFSET
0,3
COMMENTS
The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = 2 x + 1 + x/f(n-1,x), where f(0,x) = 1.
LINKS
EXAMPLE
f(0,x) = 1/1, so that p(0,x) = 1
f(1,x) = (1 + 3 x)/1, so that p(1,x) = 1 + 3 x;
f(2,x) = (1 + 6 x + 3 x^2)/(1 + 3 x), so that p(2,x) = 1 + 6 x + 3 x^2.
First 6 rows of the triangle of coefficients:
1
1 3
1 6 6
1 9 21 12
1 12 45 60 24
1 15 78 171 156 48
MATHEMATICA
z = 14; f[n_, x_] := 2 x + 1 + x/f[n - 1, x]; f[0, x_] = 1;
t = Table[Factor[f[n, x]], {n, 0, z}]
u = Numerator[t]
TableForm[Rest[Table[CoefficientList[u[[n]], x], {n, 0, z}]]] (*A249251 array*)
Flatten[CoefficientList[u, x]] (*A249251 sequence*)
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Oct 24 2014
STATUS
approved