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%I #6 Mar 30 2012 18:58:15
%S 1,1,2,1,5,5,1,5,16,13,1,5,19,48,34,1,5,19,68,141,89,1,5,19,71,233,
%T 409,233,1,5,19,71,262,772,1175,610,1,5,19,71,265,948,2492,3349,1597,
%U 1,5,19,71,265,986,3354,7879,9482,4181,1,5,19,71,265,989,3641
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209760; see the Formula section.
%C Limiting row: A001834
%C Coefficient of x^n in u(n,x): odd-indexed Fibonacci numbers
%C Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...; A033999
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%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 1...2
%e 1...5...5
%e 1...5...16...13
%e 1...5...19...48...34
%e First three polynomials u(n,x): 1, 1 + 2x, 1 + 5x + 5x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%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[%] (* A209759 *)
%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[%] (* A209760 *)
%Y Cf. A209760, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 14 2012
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