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A249248
Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
4
1, 1, 3, 1, 7, 3, 1, 12, 22, 3, 1, 18, 69, 40, 3, 1, 25, 159, 241, 61, 3, 1, 33, 310, 883, 582, 85, 3, 1, 42, 543, 2465, 3393, 1155, 112, 3, 1, 52, 882, 5798, 13805, 9786, 2032, 142, 3, 1, 63, 1354, 12110, 44253, 57521, 23368, 3294, 175, 3, 1, 75, 1989
OFFSET
1,3
COMMENTS
The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + 1 + n*x/f(n-1,x), where f(1,x) = 1.
LINKS
EXAMPLE
f(1,x) = 1/1, so that p(1,x) = 1
f(2,x) = (1 + 3 x)/1, so that p(2,x) = 1 + 3 x;
f(3,x) = (1 + 7 x + 3 x^2)/(1 + 3 x), so that p(3,x) = 1 + 7 x + 3 x^2.
First 6 rows of the triangle of coefficients:
1
1 3
1 7 3
1 12 22 3
1 18 69 40 3
1 25 150 241 61 3
MATHEMATICA
z = 14; f[n_, x_] := x + 1 + n*x/f[n - 1, x]; f[1, x_] = 1;
t = Table[Factor[f[n, x]], {n, 1, z}]
u = Numerator[t]
TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (*A249248 array*)
Flatten[CoefficientList[u, x]] (*A249248 sequence*)
PROG
(PARI) rown(n) = if (n==1, 1, x + 1 + n*x/rown(n-1));
tabl(nn) = for (n=1, nn, print(Vecrev(numerator(rown(n))))); \\ Michel Marcus, Oct 30 2014
CROSSREFS
Cf. A249247.
Sequence in context: A133115 A210192 A249755 * A104797 A130330 A050227
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Oct 24 2014
STATUS
approved