A249251 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

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

Clark Kimberling, Table of n, a(n) for n = 0..5150

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

Cf. A249247, A249248, A249250, A249252.

Sequence in context: A179069 A235706 A124847 * A127893 A127895 A325005

Adjacent sequences: A249248 A249249 A249250 * A249252 A249253 A249254

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Oct 24 2014

Status

approved