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%I #8 Mar 30 2012 18:58:15
%S 1,1,2,3,4,2,5,10,6,2,9,20,18,8,2,15,40,44,28,10,2,25,76,102,80,40,12,
%T 2,41,142,222,210,130,54,14,2,67,260,466,512,380,196,70,16,2,109,470,
%U 948,1188,1022,630,280,88,18,2,177,840,1884,2648,2590,1848,980
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209748; see the Formula section.
%C Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F v(n,x)=u(n-1,x)+v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...2
%e 3...4....2
%e 5...10...6....2
%e 9...20...18...8...2
%e First three polynomials u(n,x): 1, 1 + 2x, 3 + 4x + 2x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t v[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A209747 *)
%t Table[Expand[v[n, x]], {n, 1, z}]
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A209748 *)
%Y Cf. A209748, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 13 2012
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