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A208905 Triangle of coefficients of polynomials u(n,x) jointly generated with A208906; see the Formula section.

%I A208905 #5 Mar 30 2012 18:58:14
%S A208905 1,1,2,1,6,2,1,12,6,4,1,20,12,20,4,1,30,20,60,20,8,1,42,30,140,60,56,
%T A208905 8,1,56,42,280,140,224,56,16,1,72,56,504,280,672,224,144,16,1,90,72,
%U A208905 840,504,1680,672,720,144,32,1,110,90,1320,840,3696,1680,2640,720
%N A208905 Triangle of coefficients of polynomials u(n,x) jointly generated with A208906; see the Formula section.
%C A208905 For a discussion and guide to related arrays, see A208510.
%F A208905 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208905 v(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A208905 where u(1,x)=1, v(1,x)=1.
%e A208905 First five rows:
%e A208905 1
%e A208905 1...2
%e A208905 1...6....2
%e A208905 1...12...6....4
%e A208905 1...20...12...20...4
%e A208905 First five polynomials u(n,x):
%e A208905 1
%e A208905 1 + 2x
%e A208905 1 + 6x + 2x^2
%e A208905 1 + 12x + 6x^2 + 4x^3
%e A208905 1 + 20x + 12x^2 + 20x^3 + 4x^4
%t A208905 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208905 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208905 v[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A208905 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208905 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208905 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208905 TableForm[cu]
%t A208905 Flatten[%]  (* A208905 *)
%t A208905 Table[Expand[v[n, x]], {n, 1, z}]
%t A208905 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208905 TableForm[cv]
%t A208905 Flatten[%]  (* A208906 *)
%Y A208905 Cf. A208906, A208510.
%K A208905 nonn,tabl
%O A208905 1,3
%A A208905 _Clark Kimberling_, Mar 03 2012