A209158 - OEIS

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

%S 1,2,1,3,5,3,4,11,13,5,5,19,35,31,11,6,29,73,101,73,21,7,41,131,247,

%T 275,167,43,8,55,213,509,769,717,377,85,9,71,323,935,1787,2255,1811,

%U 839,171,10,89,465,1581,3657,5829,6321,4461,1849,341,11,109,643

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209159; 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)+x*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...5....5

%e 4...11...13...5

%e 5...19...35...31...11

%e First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 5x^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] + 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[%]    (* A209158 *)

%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[%]    (* A209159 *)

%Y Cf. A209159, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 07 2012