A209768 - OEIS

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

%S 1,2,3,3,7,7,4,14,26,17,5,24,64,83,41,6,37,130,251,250,99,7,53,233,

%T 599,899,723,239,8,72,382,1232,2478,3022,2034,577,9,94,586,2282,5774,

%U 9476,9700,5607,1393,10,119,854,3908,11952,24734,34152,30063

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209767; 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+1)*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 2...3

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

%e 4...14...26...17

%e 5...24...64...83...41

%e First three polynomials v(n,x): 1, 2 + 3x , 3 + 7x + 7x^2.

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

%t u[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%]    (* A209767 *)

%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[%]    (* A209768 *)

%Y Cf. A209667, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 15 2012