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A209151 Triangle of coefficients of polynomials u(n,x) jointly generated with A208337; see the Formula section.

%I A209151 #5 Mar 30 2012 18:58:15
%S A209151 1,2,1,3,4,2,4,8,8,3,5,13,19,15,5,6,19,36,42,28,8,7,26,60,91,89,51,13,
%T A209151 8,34,92,170,216,182,92,21,9,43,133,288,446,489,363,164,34,10,53,184,
%U A209151 455,826,1105,1068,709,290,55,11,64,246,682,1414,2219,2619
%N A209151 Triangle of coefficients of polynomials u(n,x) jointly generated with A208337; see the Formula section.
%C A209151 Last term in each row is a Fibonacci number (A000045).
%C A209151 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209151 For a discussion and guide to related arrays, see A208510.
%F A209151 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209151 v(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A209151 where u(1,x)=1, v(1,x)=1.
%e A209151 First five rows:
%e A209151 1
%e A209151 2...1
%e A209151 3...4....2
%e A209151 4...8....8....3
%e A209151 5...13...19...15...5
%e A209151 First three polynomials v(n,x): 1, 2 + x, 3 + 4x + 2x^2.
%t A209151 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209151 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209151 v[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A209151 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209151 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209151 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209151 TableForm[cu]
%t A209151 Flatten[%]    (* A209151 *)
%t A209151 Table[Expand[v[n, x]], {n, 1, z}]
%t A209151 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209151 TableForm[cv]
%t A209151 Flatten[%]    (* A208337 *)
%Y A209151 Cf. A208337, A208510.
%K A209151 nonn,tabl
%O A209151 1,2
%A A209151 _Clark Kimberling_, Mar 07 2012