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

%I A249755 #8 Nov 14 2014 21:13:42
%S A249755 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 A249755 3,1,42,98,140,126,70,22,3,1,52,140,238,266,196,92,25,3,1,63,192,378,
%U A249755 504,462,288,117,28,3,1,75,255,570,882,966,750,405,145,31
%N A249755 Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + (n + 1)*x, p(0,x) = 1.
%C A249755 (Sum of numbers in row n) = A000295(n+1) for n >= 0.
%H A249755 Clark Kimberling, <a href="/A249755/b249755.txt">Rows n = 0..100, flattened</a>
%e A249755 p(0,x) = 1
%e A249755 p(1,x) = 1 + 3*x
%e A249755 p(2,x) = 1 + 7*x + 3*x^2
%e A249755 First 6 rows:
%e A249755 1
%e A249755 1   3
%e A249755 1   7    3
%e A249755 1   12   10   3
%e A249755 1   18   22   13   3
%e A249755 1   25   40   35   16   3
%t A249755 z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + (n + 1)*x; p[0, x_] = 1;
%t A249755 t = Table[Factor[p[n, x]], {n, 0, z}]
%t A249755 TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249755 array *)
%t A249755 Flatten[CoefficientList[t, x]] (* A249755 sequence *)
%Y A249755 Cf. A249756, A249757, A000295.
%K A249755 nonn,tabl,easy
%O A249755 0,3
%A A249755 _Clark Kimberling_, Nov 07 2014