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%I #5 Mar 30 2012 18:58:15
%S 1,3,2,5,8,4,9,22,22,8,15,52,78,56,16,25,112,226,242,136,32,41,228,
%T 580,828,692,320,64,67,446,1374,2456,2726,1872,736,128,109,848,3074,
%U 6612,9158,8336,4864,1664,256,177,1578,6590,16590,27564,31250
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209773; 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)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 3....2
%e 5....8....4
%e 9....22...22...8
%e 15...52...78...56...16
%e First three polynomials v(n,x): 1, 3 + 2x , 5 + 8x + 4x^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_] := (x + 1)*u[n - 1, x] + (x + 1)*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[%] (* A209775 *)
%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[%] (* A209776 *)
%Y Cf. A209675, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 15 2012
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