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A210218 Triangle of coefficients of polynomials v(n,x) jointly generated with A210217; see the Formula section.

%I A210218 #4 Mar 30 2012 18:58:16
%S A210218 1,1,3,1,4,7,1,4,13,15,1,4,14,38,31,1,4,14,47,103,63,1,4,14,48,151,
%T A210218 264,127,1,4,14,48,163,462,649,255,1,4,14,48,164,544,1348,1546,511,1,
%U A210218 4,14,48,164,559,1768,3769,3595,1023,1,4,14,48,164,560,1893,5564
%N A210218 Triangle of coefficients of polynomials v(n,x) jointly generated with A210217; see the Formula section.
%C A210218 Limiting row:  A007070
%C A210218 For a discussion and guide to related arrays, see A208510.
%F A210218 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210218 v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,
%F A210218 where u(1,x)=1, v(1,x)=1.
%e A210218 First five rows:
%e A210218 1
%e A210218 1...3
%e A210218 1...4...7
%e A210218 1...4...13...15
%e A210218 1...4...14...38...31
%e A210218 First three polynomials v(n,x): 1, 1 + 3x , 1 + 4x + 7x^2.
%t A210218 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210218 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210218 v[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210218 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210218 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210218 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210218 TableForm[cu]
%t A210218 Flatten[%]    (* A210217 *)
%t A210218 Table[Expand[v[n, x]], {n, 1, z}]
%t A210218 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210218 TableForm[cv]
%t A210218 Flatten[%]    (* A210218 *)
%Y A210218 Cf. A210217, A208510.
%K A210218 nonn,tabl
%O A210218 1,3
%A A210218 _Clark Kimberling_, Mar 19 2012