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%I #5 Mar 30 2012 18:58:16
%S 1,2,2,3,4,4,4,6,10,8,5,8,18,22,16,6,10,28,42,50,32,7,12,40,68,106,
%T 110,64,8,14,54,100,188,250,242,128,9,16,70,138,300,468,594,526,256,
%U 10,18,88,182,446,780,1188,1378,1138,512,11,20,108,232,630,1202
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210555; see the Formula section.
%C Alternating row sums: 1,0,3,0,9,0,27,0,81,0,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2...2
%e 3...4...4
%e 4...6...10...8
%e 5...8...18...22...16
%e First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 4x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A210555 *)
%t Table[Expand[v[n, x]], {n, 1, z}]
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210556 *)
%Y Cf. A210555, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 22 2012
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