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A208919 Triangle of coefficients of polynomials u(n,x) jointly generated with A208920; see the Formula section.

%I A208919 #6 Mar 30 2012 18:58:14
%S A208919 1,1,2,1,6,6,1,12,20,14,1,20,44,66,38,1,30,80,190,208,94,1,42,130,430,
%T A208919 678,622,246,1,56,196,840,1708,2380,1852,622,1,72,280,1484,3668,6888,
%U A208919 7928,5338,1606,1,90,384,2436,7056,16716,25344,25650,15336
%N A208919 Triangle of coefficients of polynomials u(n,x) jointly generated with A208920; see the Formula section.
%C A208919 For a discussion and guide to related arrays, see A208510.
%F A208919 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208919 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A208919 where u(1,x)=1, v(1,x)=1.
%e A208919 First five rows:
%e A208919 1
%e A208919 1...2
%e A208919 1...6....6
%e A208919 1...12...20...14
%e A208919 1...20...44...66...38
%e A208919 First five polynomials u(n,x):
%e A208919 1
%e A208919 1 + 2x
%e A208919 1 + 6x + 6x^2
%e A208919 1 + 12x + 20x^2 + 14x^3
%e A208919 1 + 20x + 44x^2 + 66x^3 + 38x^4
%t A208919 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208919 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208919 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A208919 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208919 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208919 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208919 TableForm[cu]
%t A208919 Flatten[%]    (* A208919 *)
%t A208919 Table[Expand[v[n, x]], {n, 1, z}]
%t A208919 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208919 TableForm[cv]
%t A208919 Flatten[%]    (* A208920 *)
%Y A208919 Cf. A208920, A208510.
%K A208919 nonn,tabl
%O A208919 1,3
%A A208919 _Clark Kimberling_, Mar 04 2012