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A208906 Triangle of coefficients of polynomials v(n,x) jointly generated with A208905; see the Formula section.

%I A208906 #5 Mar 30 2012 18:58:14
%S A208906 1,2,1,3,2,2,4,3,8,2,5,4,20,8,4,6,5,40,20,24,4,7,6,70,40,84,24,8,8,7,
%T A208906 112,70,224,84,64,8,9,8,168,112,504,224,288,64,16,10,9,240,168,1008,
%U A208906 504,960,288,160,16,11,10,330,240,1848,1008,2640,960,880,160,32
%N A208906 Triangle of coefficients of polynomials v(n,x) jointly generated with A208905; see the Formula section.
%C A208906 For a discussion and guide to related arrays, see A208510.
%F A208906 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208906 v(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A208906 where u(1,x)=1, v(1,x)=1.
%e A208906 First five rows:
%e A208906 1
%e A208906 2...1
%e A208906 3...2...2
%e A208906 4...3...8....2
%e A208906 5...4...20...8...4
%e A208906 First five polynomials v(n,x):
%e A208906 1
%e A208906 2 + x
%e A208906 3 + 2x + 2x^2
%e A208906 4 + 3x + 8x^2 + 2x^3
%e A208906 5 + 4x + 20x^2 + 8x^3 + 4x^4
%t A208906 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208906 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208906 v[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A208906 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208906 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208906 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208906 TableForm[cu]
%t A208906 Flatten[%]    (* A208905 *)
%t A208906 Table[Expand[v[n, x]], {n, 1, z}]
%t A208906 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208906 TableForm[cv]
%t A208906 Flatten[%]    (* A208906 *)
%Y A208906 Cf. A208905, A208510.
%K A208906 nonn,tabl
%O A208906 1,2
%A A208906 _Clark Kimberling_, Mar 03 2012