A209752 - OEIS

%I #5 Mar 30 2012 18:58:15

%S 1,2,2,2,6,4,3,9,16,8,3,16,33,40,16,4,20,67,105,96,32,4,30,103,242,

%T 305,224,64,5,35,169,441,793,833,512,128,5,48,230,792,1664,2424,2177,

%U 1152,256,6,54,338,1230,3272,5736,7031,5505,2560,512,6,70,430

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209751; see the Formula section.

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

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

%F v(n,x)=u(n-1,x)+2x*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 2...6....4

%e 3...9....16...8

%e 3...16...33...40...16

%e First three polynomials v(n,x): 1, 2 + 2x , 2 + 6x + 4x^2.

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

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

%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[%]    (* A209751 *)

%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[%]    (* A209752 *)

%Y Cf. A209651, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 14 2012