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Triangle of coefficients of polynomials v(n,x) jointly generated with A207633; see Formula section.
3

%I #5 Mar 30 2012 18:58:13

%S 1,2,3,3,6,6,5,13,15,12,8,26,41,36,24,13,50,95,115,84,48,21,94,210,

%T 300,302,192,96,34,173,443,740,871,760,432,192,55,314,905,1716,2353,

%U 2392,1856,960,384,89,563,1803,3823,5916,6987,6312,4432,2112,768

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A207633; 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...3

%e 3...6....6

%e 5...13...15...12

%e 8...26...41...36...24

%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] + 2 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[%] (* A207633 *)

%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[%] (* A207634 *)

%Y Cf. A207633.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Feb 24 2012