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A210602 Triangle of coefficients of polynomials v(n,x) jointly generated with A210597; see the Formula section.

%I A210602 #5 Mar 30 2012 18:58:17
%S A210602 1,3,1,6,5,2,11,14,11,4,19,34,36,24,8,32,74,101,89,52,16,53,152,251,
%T A210602 279,214,112,32,87,299,582,769,735,504,240,64,142,571,1279,1961,2208,
%U A210602 1872,1168,512,128,231,1066,2704,4706,6096,6057,4648,2672,1088
%N A210602 Triangle of coefficients of polynomials v(n,x) jointly generated with A210597; see the Formula section.
%C A210602 For n>1, row n starts with F(n+3)-2, where F=A000045
%C A210602 (Fibonacci numbers), and ends with 2^(n-2).
%C A210602 For a discussion and guide to related arrays, see A208510.
%F A210602 u(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A210602 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A210602 where u(1,x)=1, v(1,x)=1.
%e A210602 First five rows:
%e A210602 1
%e A210602 3....1
%e A210602 6....5....2
%e A210602 11...14...11...4
%e A210602 19...34...36...24...8
%e A210602 First three polynomials v(n,x): 1, 3 + x, 6 + 5x + 2x^2
%t A210602 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210602 u[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210602 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A210602 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210602 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210602 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210602 TableForm[cu]
%t A210602 Flatten[%]    (* A210597 *)
%t A210602 Table[Expand[v[n, x]], {n, 1, z}]
%t A210602 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210602 TableForm[cv]
%t A210602 Flatten[%]    (* A210602 *)
%Y A210602 Cf. A210597, A208510.
%K A210602 nonn,tabl
%O A210602 1,2
%A A210602 _Clark Kimberling_, Mar 24 2012