A249758 Triangular array of coefficients of polynomials p(n,x) = (x + 2)*p(n-1,x) + x, p(0,x) = 1.

1, 2, 2, 4, 7, 2, 8, 19, 11, 2, 16, 47, 41, 15, 2, 32, 111, 129, 71, 19, 2, 64, 255, 369, 271, 109, 23, 2, 128, 575, 993, 911, 489, 155, 27, 2, 256, 1279, 2561, 2815, 1889, 799, 209, 31, 2, 512, 2815, 6401, 8191, 6593, 3487, 1217, 271, 35, 2, 1024, 6143

Offset: 0

Author

Clark Kimberling, Nov 07 2014

Keywords

• nonn
• tabl
• easy

Examples

			p(0,x) = 1
p(1,x) = 2 + 2*x
p(2,x) = 4 + 7*x + 2*x^2
First 6 rows:
1
2    2
4    7     2
8    19    11    2
16   47    41    15    2
32   111   129   71    19   2
		

Links

• Clark Kimberling, Rows n = 0..100, flattened

Crossrefs

Cf. A249755, A249756.

Programs

Mathematica

z = 14; p[n_, x_] := (x + 2) p[n - 1, x] + x; p[0, x_] = 1;
t = Table[Factor[p[n, x]], {n, 0, z}]
TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249758 array *)
Flatten[CoefficientList[t, x]] (* A249758 sequence *)