A249247 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

1, 1, 1, 2, 3, 6, 10, 1, 24, 42, 7, 120, 216, 45, 1, 720, 1320, 312, 13, 5040, 9360, 2400, 136, 1, 40320, 75600, 20520, 1400, 21, 362880, 685440, 194040, 15000, 325, 1, 3628800, 6894720, 2016000, 170520, 4650, 31, 39916800, 76204800, 22861440, 2069760, 66150

Offset

1,4

Comments

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = n - 1 + x/f(n-1,x), where f(n,1) = 1.

Links

Clark Kimberling, Table of n, a(n) for n = 1..2600

Example

f(1,x) = 1/1, so that p(1,x) = 1
f(2,x) = (1 + x)/1, so that p(2,x) = 1 + x;
f(3,x) = (2 + 3 x)/(1 + x), so that p(3,x) = 2 + 3 x.
First 7 rows of the triangle of coefficients:
1
1    1
2    3
6    10    1
24   42    7
120  216   45    1
720  1320  312   13

Mathematica

z = 14; f[n_, x_] := n - 1 + 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}]] (* A249247 array *)
v = Flatten[CoefficientList[u, x]] (* A249247 sequence *)

Crossrefs

Cf. A249248.

Sequence in context: A077753 A353122 A058911 * A276956 A276946 A191542

Adjacent sequences: A249244 A249245 A249246 * A249248 A249249 A249250

Keyword

nonn,tabf,easy

Author

Clark Kimberling, Oct 24 2014

Status

approved