A209157 - OEIS

%I #7 Jul 12 2012 00:40:00

%S 1,2,2,3,6,2,4,14,12,4,5,28,40,24,4,6,50,104,96,40,8,7,82,234,304,204,

%T 72,8,8,126,476,820,768,408,112,16,9,184,896,1968,2408,1760,768,192,

%U 16,10,258,1584,4320,6640,6288,3776,1408,288,32,11,350,2658

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209154; see the Formula section.

%C Last number of each row is a power of 2.

%C (n-th alternating row sum)=2-n for n>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)+v(n-1,x)+1,

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

%e First five rows:

%e 1

%e 2...2

%e 3...6....2

%e 4...14...12...4

%e 5...28...40...24...4

%e First three polynomials v(n,x): 1, 2 + 2x, 3 + 6x + x^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] + 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[%]    (* A209154 *)

%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[%]    (* A209157 *)

%Y Cf. A209154, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 07 2012