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A209691 Triangle of coefficients of polynomials u(n,x) jointly generated with A209692; see the Formula section.

%I A209691 #5 Mar 30 2012 18:58:15
%S A209691 1,0,2,0,2,4,0,1,8,8,0,1,5,24,16,0,1,4,21,64,32,0,1,4,15,77,160,64,0,
%T A209691 1,4,14,58,253,384,128,0,1,4,14,49,221,765,896,256,0,1,4,14,48,177,
%U A209691 800,2173,2048,512,0,1,4,14,48,165,654,2723,5885,4608,1024,0,1,4
%N A209691 Triangle of coefficients of polynomials u(n,x) jointly generated with A209692; see the Formula section.
%C A209691 Combinatorial limit of rows:  A007070.
%C A209691 For a discussion and guide to related arrays, see A208510.
%F A209691 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209691 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A209691 where u(1,x)=1, v(1,x)=1.
%e A209691 First five rows:
%e A209691 1
%e A209691 0...2
%e A209691 0...2...4
%e A209691 0...1...8...8
%e A209691 0...1...5...24...16
%e A209691 First three polynomials v(n,x): 1, 2x, 2x + 4x^2.
%t A209691 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209691 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t A209691 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209691 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209691 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209691 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209691 TableForm[cu]
%t A209691 Flatten[%]   (* A209691 *)
%t A209691 Table[Expand[v[n, x]], {n, 1, z}]
%t A209691 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209691 TableForm[cv]
%t A209691 Flatten[%]   (* A209692 *)
%Y A209691 Cf. A209692, A208510.
%K A209691 nonn,tabl
%O A209691 1,3
%A A209691 _Clark Kimberling_, Mar 12 2012