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%I #5 Mar 30 2012 18:58:15
%S 1,2,1,5,5,1,11,15,6,1,23,41,27,9,1,47,105,95,45,10,1,95,257,295,185,
%T 65,13,1,191,609,847,665,315,91,14,1,383,1409,2303,2177,1295,497,119,
%U 17,1,767,3201,6015,6657,4767,2289,735,153,18,1,1535,7169,15231
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209165; see the Formula section.
%C Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=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 2....1
%e 5....5....1
%e 11...15...6....1
%e 23...41...27...9...1
%e First three polynomials v(n,x): 1, 2 + x, 5 + 5x + 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. A209165, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 08 2012
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