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A209697 Triangle of coefficients of polynomials u(n,x) jointly generated with A209698; see the Formula section.

%I A209697 #5 Mar 30 2012 18:58:15
%S A209697 1,0,2,0,2,4,0,3,6,8,0,4,10,16,16,0,5,15,30,40,32,0,6,21,50,84,96,64,
%T A209697 0,7,28,77,154,224,224,128,0,8,36,112,258,448,576,512,256,0,9,45,156,
%U A209697 405,810,1248,1440,1152,512,0,10,55,210,605,1362,2420,3360,3520
%N A209697 Triangle of coefficients of polynomials u(n,x) jointly generated with A209698; see the Formula section.
%C A209697 For a discussion and guide to related arrays, see A208510.
%F A209697 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209697 v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209697 where u(1,x)=1, v(1,x)=1.
%e A209697 First five rows:
%e A209697 1
%e A209697 0...2
%e A209697 0...2....4
%e A209697 0...3....6...8
%e A209697 0...4...10...16...16
%e A209697 First three polynomials v(n,x): 1, 2x, 2x + 4x^2.
%t A209697 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209697 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t A209697 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209697 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209697 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209697 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209697 TableForm[cu]
%t A209697 Flatten[%]   (* A209697 *)
%t A209697 Table[Expand[v[n, x]], {n, 1, z}]
%t A209697 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209697 TableForm[cv]
%t A209697 Flatten[%]   (* A209698 *)
%Y A209697 Cf. A209698, A208510.
%K A209697 nonn,tabl
%O A209697 1,3
%A A209697 _Clark Kimberling_, Mar 12 2012