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Triangle of coefficients of polynomials v(n,x) jointly generated with A210035; see the Formula section.
3

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

%S 1,2,2,4,4,4,7,10,8,8,12,20,24,16,16,20,40,52,56,32,32,33,76,116,128,

%T 128,64,64,54,142,240,312,304,288,128,128,88,260,488,688,800,704,640,

%U 256,256,143,470,964,1496,1856,1984,1600,1408,512,512,232,840

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210035; 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)=u(n-1,x)+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 4....4....4

%e 7....10...8....8

%e 12...20...24...16...16

%e First three polynomials v(n,x): 1, 2 + 2x , 4 + 4x + 4x^2.

%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_] := u[n - 1, x] + 2 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[%] (* A210035 *)

%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[%] (* A210036 *)

%Y Cf. A210035, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 16 2012