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%I #5 Mar 30 2012 18:58:15
%S 1,2,2,2,5,4,3,9,14,8,3,14,32,36,16,4,20,60,100,88,32,4,27,100,220,
%T 288,208,64,5,35,154,420,728,784,480,128,5,44,224,728,1568,2240,2048,
%U 1088,256,6,54,312,1176,3024,5376,6528,5184,2432,512,6,65,420
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209771; see the Formula section.
%C Alternating row sums: 1,0,1,0,1,0,1,0,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F v(n,x)=(x+1)*u(n-1,x)+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 2...5....4
%e 3...9....14...8
%e 3...14...32...36...16
%e First three polynomials v(n,x): 1, 2 + 2x , 2 + 5x + 4x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A209771 *)
%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[%] (* A209772 *)
%Y Cf. A209671, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 15 2012
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