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A209701 Triangle of coefficients of polynomials u(n,x) jointly generated with A209702; see the Formula section.

%I A209701 #5 Mar 30 2012 18:58:15
%S A209701 1,0,2,0,2,5,0,3,7,12,0,4,11,23,29,0,5,16,41,70,70,0,6,22,66,140,204,
%T A209701 169,0,7,29,99,247,455,577,408,0,8,37,141,401,875,1423,1597,985,0,9,
%U A209701 46,193,613,1529,2965,4321,4348,2378,0,10,56,256,895,2495,5549
%N A209701 Triangle of coefficients of polynomials u(n,x) jointly generated with A209702; see the Formula section.
%C A209701 For a discussion and guide to related arrays, see A208510.
%F A209701 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209701 v(n,x)=2x*u(n-1,x)+(x+1)v(n-1,x)+1,
%F A209701 where u(1,x)=1, v(1,x)=1.
%e A209701 First five rows:
%e A209701 1
%e A209701 0...2
%e A209701 0...2...5
%e A209701 0...3...7....12
%e A209701 0...4...11...23...29
%e A209701 First three polynomials v(n,x): 1, 2x, 2x + 5x^2.
%t A209701 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209701 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t A209701 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209701 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209701 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209701 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209701 TableForm[cu]
%t A209701 Flatten[%]  (* A209701 *)
%t A209701 Table[Expand[v[n, x]], {n, 1, z}]
%t A209701 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209701 TableForm[cv]
%t A209701 Flatten[%]  (* A209702 *)
%Y A209701 Cf. A209702, A208510.
%K A209701 nonn,tabl
%O A209701 1,3
%A A209701 _Clark Kimberling_, Mar 12 2012