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A209752 Triangle of coefficients of polynomials v(n,x) jointly generated with A209751; see the Formula section.

%I A209752 #5 Mar 30 2012 18:58:15
%S A209752 1,2,2,2,6,4,3,9,16,8,3,16,33,40,16,4,20,67,105,96,32,4,30,103,242,
%T A209752 305,224,64,5,35,169,441,793,833,512,128,5,48,230,792,1664,2424,2177,
%U A209752 1152,256,6,54,338,1230,3272,5736,7031,5505,2560,512,6,70,430
%N A209752 Triangle of coefficients of polynomials v(n,x) jointly generated with A209751; see the Formula section.
%C A209752 For a discussion and guide to related arrays, see A208510.
%F A209752 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209752 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A209752 where u(1,x)=1, v(1,x)=1.
%e A209752 First five rows:
%e A209752 1
%e A209752 2...2
%e A209752 2...6....4
%e A209752 3...9....16...8
%e A209752 3...16...33...40...16
%e A209752 First three polynomials v(n,x): 1, 2 + 2x , 2 + 6x + 4x^2.
%t A209752 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209752 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209752 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209752 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209752 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209752 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209752 TableForm[cu]
%t A209752 Flatten[%]    (* A209751 *)
%t A209752 Table[Expand[v[n, x]], {n, 1, z}]
%t A209752 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209752 TableForm[cv]
%t A209752 Flatten[%]    (* A209752 *)
%Y A209752 Cf. A209651, A208510.
%K A209752 nonn,tabl
%O A209752 1,2
%A A209752 _Clark Kimberling_, Mar 14 2012