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Triangle of coefficients of polynomials v(n,x) jointly generated with A208520; see the Formula section.
3

%I #5 Mar 30 2012 18:58:13

%S 1,2,2,3,4,2,4,6,8,4,5,8,20,16,4,6,10,40,40,24,8,7,12,70,80,84,48,8,8,

%T 14,112,140,224,168,64,16,9,16,168,224,504,448,288,128,16,10,18,240,

%U 336,1008,1008,960,576,160,32,11,20,330,480,1848,2016,2640,1920

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208520; see the Formula section.

%F u(n,x)=u(n-1,x)+x*v(n-1,x),

%F v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,

%F where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 2...2

%e 3...4...2

%e 4...6...8....4

%e 5...8...20...16...4

%e First five polynomials v(n,x):

%e 1

%e 2 + 2x

%e 3 + 4x + 2x^2

%e 4 + 6x + 8x^2 + 4x^3

%e 5 + 8x + 20x^2 + 16x^3 + 4x^4

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];

%t v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 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[%] (* A208520 *)

%t Table[Expand[v[n, x]], {n, 1, z}]

%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

%t TableForm[cv]

%t Flatten[%] (* A208521 *)

%Y Cf. A208520.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Feb 28 2012