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A208917 Triangle of coefficients of polynomials u(n,x) jointly generated with A208918; see the Formula section.

%I A208917 #6 Mar 30 2012 18:58:14
%S A208917 1,1,2,1,4,8,1,6,16,24,1,8,24,56,80,1,10,32,96,208,256,1,12,40,144,
%T A208917 384,736,832,1,14,48,200,608,1472,2624,2688,1,16,56,264,880,2496,5632,
%U A208917 9216,8704,1,18,64,336,1200,3840,10112,21120,32256,28160,1,20,72
%N A208917 Triangle of coefficients of polynomials u(n,x) jointly generated with A208918; see the Formula section.
%C A208917 For a discussion and guide to related arrays, see A208510.
%F A208917 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208917 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A208917 where u(1,x)=1, v(1,x)=1.
%e A208917 First five rows:
%e A208917 1
%e A208917 1...2
%e A208917 1...4...8
%e A208917 1...6...16...24
%e A208917 1...8...24...56...80
%e A208917 First five polynomials u(n,x):
%e A208917 1
%e A208917 1 + 2x
%e A208917 1 + 4x + 8x^2
%e A208917 1 + 6x + 16x^2 + 24x^3
%e A208917 1 + 8x + 24x^2 + 56x^3 + 80x^4
%t A208917 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208917 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208917 v[n_, x_] := 2 x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A208917 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208917 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208917 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208917 TableForm[cu]
%t A208917 Flatten[%]    (* A208917 *)
%t A208917 Table[Expand[v[n, x]], {n, 1, z}]
%t A208917 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208917 TableForm[cv]
%t A208917 Flatten[%]    (* A208918 *)
%Y A208917 Cf. A208918, A208510.
%K A208917 nonn,tabl
%O A208917 1,3
%A A208917 _Clark Kimberling_, Mar 04 2012