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%I #6 Mar 30 2012 18:58:13
%S 1,2,2,3,4,2,5,9,6,2,8,18,17,8,2,13,35,41,27,10,2,21,66,93,76,39,12,2,
%T 34,122,200,196,125,53,14,2,55,222,415,472,360,190,69,16,2,89,399,837,
%U 1083,957,603,273,87,18,2,144,710,1651,2392,2400,1750,945,376
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A207631; see Formula section.
%C Column 1: Fibonacci numbers, A000045.
%F u(n,x)=u(n-1,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 3...4....2
%e 5...9....6....2
%e 8...18...17...8...2
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1
%t Table[Factor[u[n, x]], {n, 1, z}]
%t Table[Factor[v[n, x]], {n, 1, z}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A207631 *)
%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[%] (* A207632 *)
%Y Cf. A207631.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Feb 23 2012
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