A210034 - OEIS

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

%S 1,2,1,4,2,1,7,5,2,1,12,10,6,2,1,20,20,13,7,2,1,33,38,29,16,8,2,1,54,

%T 71,60,39,19,9,2,1,88,130,122,86,50,22,10,2,1,143,235,241,187,116,62,

%U 25,11,2,1,232,420,468,392,267,150,75,28,12,2,1,376,744,894,806

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210033; 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....1

%e 4....2....1

%e 7....5....2...1

%e 12...10...6...2...1

%t First three polynomials v(n,x): 1, 2 + x , 4 + 2x + x^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] + 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[%]    (* A210033 *)

%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[%]    (* A210034 *)

%Y Cf. A210033, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 16 2012