editing

approved

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

Cf. A249755, A079583.

proposed

editing

editing

proposed

allocated for Clark KimberlingTriangular 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

0,3

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

Clark Kimberling, <a href="/A249756/b249756.txt">Rows n = 0..100, flattened</a>

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

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 *)

Cf. A249755.

allocated

nonn,tabl,easy

Clark Kimberling, Nov 07 2014

approved

editing

allocated for Clark Kimberling

allocated

approved