A209565 - OEIS

%I #7 Mar 30 2012 18:58:15

%S 1,1,1,1,4,1,1,4,11,1,1,4,14,26,1,1,4,14,45,57,1,1,4,14,48,133,120,1,

%T 1,4,14,48,161,366,247,1,1,4,14,48,164,520,952,502,1,1,4,14,48,164,

%U 557,1604,2371,1013,1,1,4,14,48,164,560,1863,4724,5711,2036,1,1,4

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209566; 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),

%F v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,

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

%e First five rows:

%e 1

%e 1...1

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

%e 1...4....11...1

%e 1...4...14...26...1

%e First three polynomials v(n,x): 1, 1 + x, 1 + 4x + 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];

%t v[n_, x_] := x*u[n - 1, x] + 2 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[%]   (* A209565 *)

%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[%]   (* A209566 *)

%Y Cf. A209566, A208510.

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_, Mar 10 2012