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Triangle of coefficients of polynomials v(n,x) jointly generated with A210213; see the Formula section.
3

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

%S 1,3,1,6,5,1,11,14,7,1,19,34,25,9,1,32,74,75,39,11,1,53,152,195,139,

%T 56,13,1,87,299,468,419,231,76,15,1,142,571,1056,1147,791,356,99,17,1,

%U 231,1066,2280,2911,2429,1364,519,125,19,1,375,1956,4755,6991

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210213; 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)+1,

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

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

%e First five rows:

%e 1

%e 3....1

%e 6....5....1

%e 11...14...7....1

%e 19...34...25...9...1

%e First three polynomials v(n,x): 1, 3 + x , 6 + 5x + x^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] + 1;

%t v[n_, x_] := u[n - 1, x] + (x + 1)*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[%] (* A210213 *)

%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[%] (* A210214 *)

%Y Cf. A210213, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 19 2012