A208921 - OEIS

%I #7 Mar 30 2012 18:58:14

%S 1,1,2,1,8,2,1,18,10,4,1,32,36,28,4,1,50,100,108,36,8,1,72,230,324,

%T 196,80,8,1,98,462,840,772,440,104,16,1,128,840,1960,2456,1840,752,

%U 208,16,1,162,1416,4200,6744,6464,3824,1488,272,32,1,200,2250,8376

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208922; see the Formula section.

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

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

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

%e 1...8....2

%e 1...18...10...4

%e 1...32...36...28...4

%e First five polynomials u(n,x):

%e 1

%e 1 + 2x

%e 1 + 8x + 2x^2

%e 1 + 18x + 10x^2 + 4x^3

%e 1 + 32x + 36x^2 + 28x^3 + 4x^4

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

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

%t v[n_, x_] := (x + 1)*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[%]    (* A208921 *)

%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[%]    (* A208922 *)

%Y Cf. A208922, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 04 2012