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%I #10 Apr 20 2012 21:20:19
%S 1,3,5,3,7,8,6,9,15,19,12,11,24,41,44,24,13,35,74,107,100,48,15,48,
%T 120,214,270,224,96,17,63,181,380,591,664,496,192,19,80,259,622,1137,
%U 1576,1600,1088,384,21,99,356,959,2001,3259,4088,3792,2368,768,23
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209758; see the Formula section.
%C Row sums: even-indexed Fibonacci numbers: 1,3,8,21,55,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F v(n,x)=x*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
%e 5...3
%e 7...8....6
%e 9...15...19...12
%e First three polynomials u(n,x): 1, 3, 5 + 3x.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t v[n_, x_] := x*u[n - 1, x] + 2 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[%] (* A210041 *)
%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[%] (* A209758 *)
%Y Cf. A209758, A208510.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Mar 17 2012
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