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%I #5 Mar 30 2012 18:58:15
%S 1,2,2,3,2,4,4,2,8,8,5,2,14,16,16,6,2,22,26,40,32,7,2,32,38,78,88,64,
%T 8,2,44,52,134,178,200,128,9,2,58,68,212,310,446,440,256,10,2,74,86,
%U 316,492,846,1042,968,512,11,2,92,106,450,732,1452,2062,2462
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209699; see the Formula section.
%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),
%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...2...4
%e 4...2...8....8
%e 5...2...14...16...16
%e First three polynomials v(n,x): 1, 2 + 2x , 3 + 2x + 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];
%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[%] (* A209699 *)
%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[%] (* A209700 *)
%Y Cf. A209699, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 12 2012
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