A209558 - OEIS

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

%S 1,2,2,2,5,4,3,7,11,8,3,13,21,23,16,4,15,44,57,47,32,4,24,60,129,145,

%T 95,64,5,26,108,207,346,353,191,128,5,38,130,405,646,875,833,383,256,

%U 6,40,212,545,1345,1877,2124,1921,767,512,6,55,240,965,2021

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209557; see the Formula section.

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

%F u(n,x)=x*u(n-1,x)+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...5...4

%e 3...7...11...8

%e 3...13...21...23...16

%e First three polynomials v(n,x): 1, 2 + 2x , 2+ 5x + 4x^2 .

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

%t u[n_, x_] := x*u[n - 1, x] + 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[%]    (* A209557 *)

%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[%]    (* A209558 *)

%Y Cf. A209557, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 10 2012