A209161 - OEIS

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

%S 1,1,4,1,6,10,1,8,24,28,1,10,42,88,76,1,12,64,188,300,208,1,14,90,336,

%T 760,984,568,1,16,120,540,1560,2880,3136,1552,1,18,154,808,2820,6672,

%U 10416,9792,4240,1,20,192,1148,4676,13392,26880,36384,30096

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209160; see the Formula section.

%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 1...4

%e 1...6...10

%e 1...8...24...28

%e 1...10...42...88...76

%e First three polynomials v(n,x): 1, 1 + 4x, 1 + 6x + 10x^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. A209160, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 07 2012