A209701 - OEIS

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

%S 1,0,2,0,2,5,0,3,7,12,0,4,11,23,29,0,5,16,41,70,70,0,6,22,66,140,204,

%T 169,0,7,29,99,247,455,577,408,0,8,37,141,401,875,1423,1597,985,0,9,

%U 46,193,613,1529,2965,4321,4348,2378,0,10,56,256,895,2495,5549

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209702; 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*v(n-1,x),

%F v(n,x)=2x*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 0...2

%e 0...2...5

%e 0...3...7....12

%e 0...4...11...23...29

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

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

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

%t v[n_, x_] := 2 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[%]  (* A209701 *)

%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[%]  (* A209702 *)

%Y Cf. A209702, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 12 2012