A210194 - OEIS

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

%S 1,2,3,3,11,3,4,26,20,3,5,50,74,29,3,6,85,204,149,38,3,7,133,469,547,

%T 251,47,3,8,196,952,1618,1160,380,56,3,9,276,1764,4110,4234,2124,536,

%U 65,3,10,375,3048,9318,13036,9262,3520,719,74,3,11,495,4983

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210193; 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)=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...11...3

%e 4...26...20...3

%e 5...50...74...29...3

%e First three polynomials v(n,x): 1, 2 + 3x , 3 + 11x + 3x^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_] := 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[%]   (* A210193 *)

%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[%]  (* A210194 *)

%Y Cf. A210193, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 18 2012