A249756 - OEIS

%I #5 Nov 14 2014 21:13:05

%S 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,

%T 35,77,105,91,49,15,2,1,44,112,182,196,140,64,17,2,1,54,156,294,378,

%U 336,204,81,19,2,1,65,210,450,672,714,540,285,100,21,2,1

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

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

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

%e p(0,x) = 1

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

%e p(2,x) = 1 + 5*x + 2*x^2

%e First 6 rows:

%e 1

%e 1   2

%e 1   5    2

%e 1   9    7    2

%e 1   14   16   9    2

%e 1   20   30   25   11   2

%t z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + n*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}]]] (* A249756 array *)

%t Flatten[CoefficientList[t, x]] (* A249756 sequence *)

%Y Cf. A249755, A079583.

%K nonn,tabl,easy

%O 0,3

%A _Clark Kimberling_, Nov 07 2014