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A209699 Triangle of coefficients of polynomials u(n,x) jointly generated with A209700; see the Formula section.

%I A209699 #5 Mar 30 2012 18:58:15
%S A209699 1,0,2,0,2,4,0,3,4,8,0,4,5,12,16,0,5,6,19,28,32,0,6,7,28,45,68,64,0,7,
%T A209699 8,39,66,123,156,128,0,8,9,52,91,200,301,356,256,0,9,10,67,120,303,
%U A209699 510,747,796,512,0,10,11,84,153,436,795,1356,1789,1764,1024,0,11
%N A209699 Triangle of coefficients of polynomials u(n,x) jointly generated with A209700; see the Formula section.
%C A209699 For a discussion and guide to related arrays, see A208510.
%F A209699 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209699 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A209699 where u(1,x)=1, v(1,x)=1.
%e A209699 First five rows:
%e A209699 1
%e A209699 0...2
%e A209699 0...2...4
%e A209699 0...3...4...8
%e A209699 0...4...5...12...16
%e A209699 First three polynomials v(n,x): 1, 2x, 2x + 4x^2.
%t A209699 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209699 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t A209699 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A209699 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209699 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209699 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209699 TableForm[cu]
%t A209699 Flatten[%]    (* A209699 *)
%t A209699 Table[Expand[v[n, x]], {n, 1, z}]
%t A209699 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209699 TableForm[cv]
%t A209699 Flatten[%]   (* A209700 *)
%Y A209699 Cf. A209700, A208510.
%K A209699 nonn,tabl
%O A209699 1,3
%A A209699 _Clark Kimberling_, Mar 12 2012