A249757 Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + 2*n*x, p(0,x) = 1.

1, 1, 3, 1, 8, 3, 1, 15, 11, 3, 1, 24, 26, 14, 3, 1, 35, 50, 40, 17, 3, 1, 48, 85, 90, 57, 20, 3, 1, 63, 133, 175, 147, 77, 23, 3, 1, 80, 196, 308, 322, 224, 100, 26, 3, 1, 99, 276, 504, 630, 546, 324, 126, 29, 3, 1, 120, 375, 780, 1134, 1176, 870, 450, 155

Offset: 0

Author

Clark Kimberling, Nov 07 2014

Keywords

• nonn
• tabl
• easy

Comments

(Sum of numbers in row n) = A097809(n) for n >= 0.

Examples

			p(0,x) = 1
p(1,x) = 1 + 3*x
p(2,x) = 1 + 8*x + 3*x^2
First 6 rows:
1
1   3
1   8    3
1   15   11    3
1   24   26    14   3
1   35   50    40   17   3
		

Links

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

Crossrefs

Cf. A249755, A249756, A097809.

Programs

Mathematica

z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + 2*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}]]] (* A249757 array *)
Flatten[CoefficientList[t, x]] (* A249757 sequence *)