%I #5 Mar 30 2012 18:58:15
%S 1,3,1,6,4,1,12,14,7,1,24,40,28,8,1,48,104,96,44,11,1,96,256,296,184,
%T 66,12,1,192,608,848,664,316,90,15,1,384,1408,2304,2176,1296,496,120,
%U 16,1,768,3200,6016,6656,4768,2288,736,152,19,1,1536,7168,15232
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209164; see the Formula section.
%C Alternating row sums: 1,2,3,4,5,6,7,8,9,10,11,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F v(n,x)=(x+1)*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 3....1
%e 6....4....1
%e 12...14...7....1
%e 24...40...28...8...1
%e First three polynomials v(n,x): 1, 3 + x, 6 + 4x + x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t v[n_, x_] := (x + 1)*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[%] (* A209164 *)
%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[%] (* A209165 *)
%Y Cf. A209164, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 08 2012
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