login
Triangle of coefficients of polynomials v(n,x) jointly generated with A210191; see the Formula section.
3

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

%S 1,1,3,1,7,3,1,11,13,3,1,15,31,19,3,1,19,57,63,25,3,1,23,91,151,107,

%T 31,3,1,27,133,299,321,163,37,3,1,31,183,523,771,591,231,43,3,1,35,

%U 241,839,1593,1683,985,311,49,3,1,39,307,1263,2955,4047,3259,1527

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210191; 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)+x*v(n-1,x)+1,

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

%e First five rows:

%e 1

%e 1...3

%e 1...7....3

%e 1...11...13...3

%e 1...15...31...19...3

%e First three polynomials v(n,x): 1, 1 + 3x , 1 + 7x + 3x^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_] := 2 x*u[n - 1, x] + 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[%] (* A210191 *)

%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[%] (* A210192 *)

%Y Cf. A210191, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 18 2012