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%I #7 Mar 30 2012 18:58:15
%S 1,2,1,5,4,11,11,1,23,28,6,47,68,23,1,95,160,74,8,191,368,216,39,1,
%T 383,832,592,152,10,767,1856,1552,520,59,1,1535,4096,3936,1632,270,12,
%U 3071,8960,9728,4816,1060,83,1,6143,19456,23552,13568,3752,436
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209144; see the Formula section.
%C Alternating row sums: 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)=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....4
%e 11...11...1
%e 23...28...6
%e First three polynomials u(n,x): 1, 2 + x, 5 + 4x
%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_] := 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[%] (* A209143 *)
%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[%] (* A209144 *)
%Y Cf. A209144, A208510.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Mar 06 2012
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