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A249756 Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + n*x, p(0,x) = 1.

%I A249756 #5 Nov 14 2014 21:13:05
%S A249756 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 A249756 35,77,105,91,49,15,2,1,44,112,182,196,140,64,17,2,1,54,156,294,378,
%U A249756 336,204,81,19,2,1,65,210,450,672,714,540,285,100,21,2,1
%N A249756 Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + n*x, p(0,x) = 1.
%C A249756 (Sum of numbers in row n) = A079583(n+1) for n >= 0.
%H A249756 Clark Kimberling, <a href="/A249756/b249756.txt">Rows n = 0..100, flattened</a>
%e A249756 p(0,x) = 1
%e A249756 p(1,x) = 1 + 2*x
%e A249756 p(2,x) = 1 + 5*x + 2*x^2
%e A249756 First 6 rows:
%e A249756 1
%e A249756 1   2
%e A249756 1   5    2
%e A249756 1   9    7    2
%e A249756 1   14   16   9    2
%e A249756 1   20   30   25   11   2
%t A249756 z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + n*x; p[0, x_] = 1;
%t A249756 t = Table[Factor[p[n, x]], {n, 0, z}]
%t A249756 TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249756 array *)
%t A249756 Flatten[CoefficientList[t, x]] (* A249756 sequence *)
%Y A249756 Cf. A249755, A079583.
%K A249756 nonn,tabl,easy
%O A249756 0,3
%A A249756 _Clark Kimberling_, Nov 07 2014