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A207634 Triangle of coefficients of polynomials v(n,x) jointly generated with A207633; see Formula section.

%I A207634 #5 Mar 30 2012 18:58:13
%S A207634 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 A207634 300,302,192,96,34,173,443,740,871,760,432,192,55,314,905,1716,2353,
%U A207634 2392,1856,960,384,89,563,1803,3823,5916,6987,6312,4432,2112,768
%N A207634 Triangle of coefficients of polynomials v(n,x) jointly generated with A207633; see Formula section.
%C A207634 Column 1: Fibonacci numbers, A000045.
%F A207634 u(n,x)=u(n-1,x)+v(n-1,x),
%F A207634 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A207634 where u(1,x)=1, v(1,x)=1.
%e A207634 First five rows:
%e A207634 1
%e A207634 2...3
%e A207634 3...6....6
%e A207634 5...13...15...12
%e A207634 8...26...41...36...24
%t A207634 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207634 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207634 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1
%t A207634 Table[Factor[u[n, x]], {n, 1, z}]
%t A207634 Table[Factor[v[n, x]], {n, 1, z}]
%t A207634 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207634 TableForm[cu]
%t A207634 Flatten[%]  (* A207633 *)
%t A207634 Table[Expand[v[n, x]], {n, 1, z}]
%t A207634 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207634 TableForm[cv]
%t A207634 Flatten[%]  (* A207634 *)
%Y A207634 Cf. A207633.
%K A207634 nonn,tabl
%O A207634 1,2
%A A207634 _Clark Kimberling_, Feb 24 2012