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%I #8 Mar 30 2012 18:58:13
%S 1,2,2,2,4,3,2,6,9,5,2,8,17,18,8,2,10,27,41,35,13,2,12,39,76,93,66,21,
%T 2,14,53,125,196,200,122,34,2,16,69,190,360,472,415,222,55,2,18,87,
%U 273,603,957,1083,837,399,89,2,20,107,376,945,1750,2400,2392
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208608; see the Formula section.
%C v(n,n)=Fibonacci(n+1)=A000045(n+1).
%F u(n,x)=u(n-1,x)+x*v(n-1,x),
%F v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2...2
%e 2...4...3
%e 2...6...9....5
%e 2...8...17...18...8
%e First five polynomials v(n,x):
%e 1
%e 2 + 2x
%e 2 + 4x + 3x^2
%e 2 + 6x + 9x^2 + 5x^3
%e 2 + 8x + 17x^2 + 18x^3 + 8x^4
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A208608 *)
%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[%] (* A208609 *)
%Y Cf. A208608.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Feb 29 2012
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