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A209767 Triangle of coefficients of polynomials u(n,x) jointly generated with A209768; see the Formula section.

%I A209767 #6 Mar 30 2012 18:58:15
%S A209767 1,1,2,2,6,5,3,12,20,12,4,21,52,63,29,5,33,109,199,187,70,6,48,200,
%T A209767 490,700,536,169,7,66,334,1032,1988,2322,1498,408,8,87,520,1948,4742,
%U A209767 7488,7378,4109,985,9,111,767,3388,10004,19992,26664,22685,11109
%N A209767 Triangle of coefficients of polynomials u(n,x) jointly generated with A209768; see the Formula section.
%C A209767 For a discussion and guide to related arrays, see A208510.
%F A209767 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209767 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209767 where u(1,x)=1, v(1,x)=1.
%e A209767 First five rows:
%e A209767 1
%e A209767 1...2
%e A209767 2...6....5
%e A209767 3...12...20...12
%e A209767 4...21...52...63...29
%e A209767 First three polynomials u(n,x): 1, 1 + 2x, 2 + 6x + 5x^2.
%t A209767 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209767 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209767 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209767 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209767 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209767 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209767 TableForm[cu]
%t A209767 Flatten[%]    (* A209767 *)
%t A209767 Table[Expand[v[n, x]], {n, 1, z}]
%t A209767 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209767 TableForm[cv]
%t A209767 Flatten[%]    (* A209768 *)
%Y A209767 Cf. A209768, A208510.
%K A209767 nonn,tabl
%O A209767 1,3
%A A209767 _Clark Kimberling_, Mar 15 2012