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A209570 Triangle of coefficients of polynomials v(n,x) jointly generated with A209569; see the Formula section.

%I A209570 #8 Mar 30 2012 18:58:15
%S A209570 1,2,2,3,4,2,4,8,8,2,5,14,20,12,2,6,22,42,40,16,2,7,32,78,102,68,20,2,
%T A209570 8,44,132,222,210,104,24,2,9,58,208,432,534,382,148,28,2,10,74,310,
%U A209570 772,1188,1126,634,200,32,2,11,92,442,1290,2392,2848,2142,982
%N A209570 Triangle of coefficients of polynomials v(n,x) jointly generated with A209569; see the Formula section.
%C A209570 For n>1, row n begins and ends with 2.
%C A209570 Alternating row sums:  1,0,1,2,1,0,1,2,1,0,1,2,...
%C A209570 For a discussion and guide to related arrays, see A208510.
%F A209570 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209570 v(n,x)=2x*u(n-1,x)+v(n-1,x) +1,
%F A209570 where u(1,x)=1, v(1,x)=1.
%e A209570 First five rows:
%e A209570 1
%e A209570 2...2
%e A209570 3...4....2
%e A209570 4...8....8....2
%e A209570 5...14...20...12...2
%e A209570 First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 2x^2.
%t A209570 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209570 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209570 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A209570 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209570 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209570 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209570 TableForm[cu]
%t A209570 Flatten[%]   (* A209569 *)
%t A209570 Table[Expand[v[n, x]], {n, 1, z}]
%t A209570 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209570 TableForm[cv]
%t A209570 Flatten[%]   (* A209570 *)
%Y A209570 Cf. A209569, A208510.
%K A209570 nonn,tabl
%O A209570 1,2
%A A209570 _Clark Kimberling_, Mar 10 2012