%I #8 Nov 14 2014 21:13:42

%S 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,

%T 3,1,42,98,140,126,70,22,3,1,52,140,238,266,196,92,25,3,1,63,192,378,

%U 504,462,288,117,28,3,1,75,255,570,882,966,750,405,145,31

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

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

%H Clark Kimberling, <a href="/A249755/b249755.txt">Rows n = 0..100, flattened</a>

%e p(0,x) = 1

%e p(1,x) = 1 + 3*x

%e p(2,x) = 1 + 7*x + 3*x^2

%e First 6 rows:

%e 1

%e 1 3

%e 1 7 3

%e 1 12 10 3

%e 1 18 22 13 3

%e 1 25 40 35 16 3

%t z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + (n + 1)*x; p[0, x_] = 1;

%t t = Table[Factor[p[n, x]], {n, 0, z}]

%t TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249755 array *)

%t Flatten[CoefficientList[t, x]] (* A249755 sequence *)

%Y Cf. A249756, A249757, A000295.

%K nonn,tabl,easy

%O 0,3

%A _Clark Kimberling_, Nov 07 2014