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%I #5 Mar 30 2012 18:58:15
%S 1,1,2,3,6,4,5,16,18,8,9,36,60,48,16,15,76,166,194,120,32,25,152,414,
%T 634,572,288,64,41,294,960,1822,2154,1584,672,128,67,554,2114,4790,
%U 7004,6752,4192,1536,256,109,1024,4476,11800,20560,24498,19952
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209776; 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+1)*v(n-1,x),
%F v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...2
%e 3...6....4
%e 5...16...18...8
%e 9...36...60...48...16
%e First three polynomials u(n,x): 1, 1 + 2x, 3 + 6x + 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 + 1)*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[%] (* A209775 *)
%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[%] (* A209776 *)
%Y Cf. A209776, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 15 2012
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