A249756 Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + n*x, p(0,x) = 1.

1, 1, 2, 1, 5, 2, 1, 9, 7, 2, 1, 14, 16, 9, 2, 1, 20, 30, 25, 11, 2, 1, 27, 50, 55, 36, 13, 2, 1, 35, 77, 105, 91, 49, 15, 2, 1, 44, 112, 182, 196, 140, 64, 17, 2, 1, 54, 156, 294, 378, 336, 204, 81, 19, 2, 1, 65, 210, 450, 672, 714, 540, 285, 100, 21, 2, 1

Offset: 0

Author

Clark Kimberling, Nov 07 2014

Keywords

• nonn
• tabl
• easy

Comments

(Sum of numbers in row n) = A079583(n+1) for n >= 0.

Examples

			p(0,x) = 1
p(1,x) = 1 + 2*x
p(2,x) = 1 + 5*x + 2*x^2
First 6 rows:
1
1   2
1   5    2
1   9    7    2
1   14   16   9    2
1   20   30   25   11   2
		

Links

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

Crossrefs

Cf. A249755, A079583.

Programs

Mathematica

z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + n*x; p[0, x_] = 1;
t = Table[Factor[p[n, x]], {n, 0, z}]
TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249756 array *)
Flatten[CoefficientList[t, x]] (* A249756 sequence *)