A209160 - OEIS

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

%S 1,2,1,3,6,4,4,13,20,10,5,22,52,62,28,6,33,104,192,192,76,7,46,180,

%T 444,680,584,208,8,61,284,870,1776,2328,1760,568,9,78,420,1530,3876,

%U 6768,7776,5256,1552,10,97,592,2492,7504,16260,24864,25464,15584

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209161; see the Formula section.

%C Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

%C For a discussion and guide to related arrays, see A208510.

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

%F v(n,x)=2x*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 2...1

%e 3...6....4

%e 4...13...20...10

%e 5...22...52...62...28

%e First three polynomials v(n,x): 1, 2 + x, 3 + 6x + 4x^2.

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

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

%t v[n_, x_] := 2 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[%]    (* A209160 *)

%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[%]    (* A209161 *)

%Y Cf. A209161, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 07 2012