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A209147 Triangle of coefficients of polynomials v(n,x) jointly generated with A209146; see the Formula section.

%I A209147 #5 Mar 30 2012 18:58:15
%S A209147 1,2,2,3,5,4,5,11,12,8,8,23,33,28,16,13,45,80,90,64,32,21,86,180,245,
%T A209147 232,144,64,34,160,387,615,696,576,320,128,55,293,801,1454,1913,1880,
%U A209147 1392,704,256,89,529,1614,3284,4902,5586,4896,3296,1536,512,144
%N A209147 Triangle of coefficients of polynomials v(n,x) jointly generated with A209146; see the Formula section.
%C A209147 Each row begins with a Fibonacci numbers and ends with a power of 2.  For a discussion and guide to related arrays, see A208510.
%F A209147 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209147 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A209147 where u(1,x)=1, v(1,x)=1.
%e A209147 First five rows:
%e A209147 1
%e A209147 2...2
%e A209147 3...5...4
%e A209147 5...11...12...8
%e A209147 8...23...33...28...16
%e A209147 First three polynomials v(n,x): 1, 2 + 2x, 3 + 5x + 4x^2.
%t A209147 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209147 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209147 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209147 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209147 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209147 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209147 TableForm[cu]
%t A209147 Flatten[%]    (* A209146 *)
%t A209147 Table[Expand[v[n, x]], {n, 1, z}]
%t A209147 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209147 TableForm[cv]
%t A209147 Flatten[%]    (* A209147 *)
%Y A209147 Cf. A209146, A208510.
%K A209147 nonn,tabl
%O A209147 1,2
%A A209147 _Clark Kimberling_, Mar 06 2012