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A210805 Triangle of coefficients of polynomials u(n,x) jointly generated with A210806; see the Formula section.

%I A210805 #5 Mar 30 2012 18:58:17
%S A210805 1,1,1,1,1,2,1,2,3,3,1,2,6,6,5,1,3,8,14,12,8,1,3,12,22,31,23,13,1,4,
%T A210805 15,37,56,65,43,21,1,4,20,52,102,132,132,79,34,1,5,24,76,160,260,296,
%U A210805 261,143,55,1,5,30,100,250,446,626,639,506,256,89,1,6,35,135,360
%N A210805 Triangle of coefficients of polynomials u(n,x) jointly generated with A210806; see the Formula section.
%C A210805 Row n starts with 1 and ends with F(n), where F=A000045 (Fibonacci numbers).
%C A210805 For a discussion and guide to related arrays, see A208510.
%F A210805 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A210805 v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x)-1,
%F A210805 where u(1,x)=1, v(1,x)=1.
%e A210805 First five rows:
%e A210805 1
%e A210805 1...1
%e A210805 1...1...2
%e A210805 1...2...3...3
%e A210805 1...2...6...6...5
%e A210805 First three polynomials u(n,x): 1, 1 + x, 1 + x + 2x^2.
%t A210805 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210805 u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
%t A210805 d[x_] := h + x; e[x_] := p + x;
%t A210805 v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
%t A210805 j = 0; c = 0; h = 2; p = -1; f = -1;
%t A210805 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210805 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210805 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210805 TableForm[cu]
%t A210805 Flatten[%]   (* A210805 *)
%t A210805 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210805 TableForm[cv]
%t A210805 Flatten[%]   (* A210806 *)
%Y A210805 Cf. A210806, A208510.
%K A210805 nonn,tabl
%O A210805 1,6
%A A210805 _Clark Kimberling_, Mar 27 2012