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