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A209771 Triangle of coefficients of polynomials u(n,x) jointly generated with A209772; see the Formula section.

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