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 A210795 Triangle of coefficients of polynomials u(n,x) jointly generated with A210796; see the Formula section. 3

%I

%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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