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%I #5 Mar 30 2012 18:58:17
%S 1,2,1,3,2,2,4,5,5,3,5,8,12,9,5,6,13,22,25,17,8,7,18,38,51,51,31,13,8,
%T 25,59,98,115,101,56,21,9,32,88,166,238,248,196,100,34,10,41,124,270,
%U 438,552,520,374,177,55,11,50,170,410,762,1090,1234,1064,704
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210796; see the Formula section.
%C Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).
%C Column 2: A000982
%C Column 3: A026035
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x),
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2...1
%e 3...2...2
%e 4...5...5....3
%e 5...8...12...9...5
%e First three polynomials u(n,x): 1, 2 + x, 3 + 2x + 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 = 1; h = 2; p = -1; f = 0;
%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[%] (* A210795 *)
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210796 *)
%Y Cf. A210796, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 26 2012
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