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A249757 Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + 2*n*x, p(0,x) = 1.

%I A249757 #5 Nov 14 2014 21:14:34
%S A249757 1,1,3,1,8,3,1,15,11,3,1,24,26,14,3,1,35,50,40,17,3,1,48,85,90,57,20,
%T A249757 3,1,63,133,175,147,77,23,3,1,80,196,308,322,224,100,26,3,1,99,276,
%U A249757 504,630,546,324,126,29,3,1,120,375,780,1134,1176,870,450,155
%N A249757 Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + 2*n*x, p(0,x) = 1.
%C A249757 (Sum of numbers in row n) = A097809(n) for n >= 0.
%H A249757 Clark Kimberling, <a href="/A249757/b249757.txt">Rows n = 0..100, flattened</a>
%e A249757 p(0,x) = 1
%e A249757 p(1,x) = 1 + 3*x
%e A249757 p(2,x) = 1 + 8*x + 3*x^2
%e A249757 First 6 rows:
%e A249757 1
%e A249757 1   3
%e A249757 1   8    3
%e A249757 1   15   11    3
%e A249757 1   24   26    14   3
%e A249757 1   35   50    40   17   3
%t A249757 z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + 2*n*x; p[0, x_] = 1;
%t A249757 t = Table[Factor[p[n, x]], {n, 0, z}]
%t A249757 TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249757 array *)
%t A249757 Flatten[CoefficientList[t, x]] (* A249757 sequence *)
%Y A249757 Cf. A249755, A249756, A097809.
%K A249757 nonn,tabl,easy
%O A249757 0,3
%A A249757 _Clark Kimberling_, Nov 07 2014