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Triangle of coefficients of polynomials v(n,x) jointly generated with A210189; see the Formula section.
3

%I #4 Mar 30 2012 18:58:16

%S 1,2,2,3,8,4,20,4,5,40,24,6,70,84,8,7,112,224,64,8,168,504,288,16,9,

%T 240,1008,960,160,10,330,1848,2640,880,32,11,440,3168,6336,3520,384,

%U 12,572,5148,13728,11440,2496,64,13,728,8008,27456,32032,11648

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210189; see the Formula section.

%C For a discussion and guide to related arrays, see A208510.

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

%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...8

%e 4...20...4

%e 5...40...24

%e First three polynomials v(n,x): 1, 2 + 2x , 3 + 8x.

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

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

%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[%] (* A210189 *)

%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[%] (* A210190 *)

%Y Cf. A210189, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 18 2012