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

%I A209768 #5 Mar 30 2012 18:58:15
%S A209768 1,2,3,3,7,7,4,14,26,17,5,24,64,83,41,6,37,130,251,250,99,7,53,233,
%T A209768 599,899,723,239,8,72,382,1232,2478,3022,2034,577,9,94,586,2282,5774,
%U A209768 9476,9700,5607,1393,10,119,854,3908,11952,24734,34152,30063
%N A209768 Triangle of coefficients of polynomials v(n,x) jointly generated with A209767; see the Formula section.
%C A209768 For a discussion and guide to related arrays, see A208510.
%F A209768 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209768 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209768 where u(1,x)=1, v(1,x)=1.
%e A209768 First five rows:
%e A209768 1
%e A209768 2...3
%e A209768 3...7....7
%e A209768 4...14...26...17
%e A209768 5...24...64...83...41
%e A209768 First three polynomials v(n,x): 1, 2 + 3x , 3 + 7x + 7x^2.
%t A209768 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209768 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209768 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209768 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209768 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209768 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209768 TableForm[cu]
%t A209768 Flatten[%]    (* A209767 *)
%t A209768 Table[Expand[v[n, x]], {n, 1, z}]
%t A209768 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209768 TableForm[cv]
%t A209768 Flatten[%]    (* A209768 *)
%Y A209768 Cf. A209667, A208510.
%K A209768 nonn,tabl
%O A209768 1,2
%A A209768 _Clark Kimberling_, Mar 15 2012