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%I #9 Dec 28 2013 04:12:44
%S 1,3,2,4,7,4,5,14,18,8,6,23,46,44,16,7,34,92,136,104,32,8,47,160,320,
%T 376,240,64,9,62,254,640,1016,992,544,128,10,79,378,1148,2296,3024,
%U 2528,1216,256,11,98,536,1904,4592,7616,8576,6272,2688,512,12,119
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209705; see the Formula section.
%C Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x) = x*u(n-1,x)+x*v(n-1,x),
%F v(n,x) = (x+1)*u(n-1,x)+(x+1)v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%F T(n,k) = 2*T(n-1,k)+2*T(n-1,k-1)-T(n-2,k)-2*T(n-2,k-1), T(1,0)=1, T(2,0)=3, T(2,1)=2, T(3,0)=4, T(3,1)=7, T(3,2)=4, T(n,k)=0 if k<0 or if k>=n. - _Philippe Deléham_, Dec 27 2013
%e First five rows:
%e 1
%e 3...2
%e 4...7....4
%e 5...14...18...8
%e 6...23...46...44...16
%e First three polynomials v(n,x): 1, 3 + 2x , 4 + 7x + 4x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + x*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[%] (* A209705 *)
%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[%] (* A209706 *)
%Y Cf. A209705, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 12 2012
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