A249755 Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + (n + 1)*x, p(0,x) = 1.

1, 1, 3, 1, 7, 3, 1, 12, 10, 3, 1, 18, 22, 13, 3, 1, 25, 40, 35, 16, 3, 1, 33, 65, 75, 51, 19, 3, 1, 42, 98, 140, 126, 70, 22, 3, 1, 52, 140, 238, 266, 196, 92, 25, 3, 1, 63, 192, 378, 504, 462, 288, 117, 28, 3, 1, 75, 255, 570, 882, 966, 750, 405, 145, 31

Offset

0,3

Comments

(Sum of numbers in row n) = A000295(n+1) for n >= 0.

Links

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

Example

p(0,x) = 1
p(1,x) = 1 + 3*x
p(2,x) = 1 + 7*x + 3*x^2
First 6 rows:
1
1   3
1   7    3
1   12   10   3
1   18   22   13   3
1   25   40   35   16   3

Mathematica

z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + (n + 1)*x; p[0, x_] = 1;
t = Table[Factor[p[n, x]], {n, 0, z}]
TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249755 array *)
Flatten[CoefficientList[t, x]] (* A249755 sequence *)

Crossrefs

Cf. A249756, A249757, A000295.

Sequence in context: A327990 A133115 A210192 * A249248 A104797 A130330

Adjacent sequences: A249752 A249753 A249754 * A249756 A249757 A249758

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Nov 07 2014

Status

approved