A208915 - OEIS

%I #5 Mar 30 2012 18:58:14

%S 1,1,2,1,4,6,1,6,12,14,1,8,18,36,38,1,10,24,66,108,94,1,12,30,104,210,

%T 308,246,1,14,36,150,344,674,892,622,1,16,42,204,510,1224,2098,2500,

%U 1606,1,18,48,266,708,1990,4024,6402,7052,4094,1,20,54,336,938

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208916; 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)=2x*u(n-1,x)+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...4...6

%e 1...6...12...14

%e 1...8...18...36...38

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

%e 1

%e 1 + 2x

%e 1 + 4x + 6x^2

%e 1 + 6x + 12x^2 + 14x^3

%e 1 + 8x + 18x^2 + 36x^3 + 38x^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_] := 2 x*u[n - 1, x] + 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[%]    (* A208915 *)

%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[%]    (* A208916 *)

%Y Cf. A208914, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 03 2012