A207624 - OEIS

%I #5 Mar 30 2012 18:58:13

%S 1,2,3,3,4,8,3,5,15,14,3,6,24,37,20,3,7,35,76,71,26,3,8,48,135,184,

%T 117,32,3,9,63,218,395,372,175,38,3,10,80,329,748,951,664,245,44,3,11,

%U 99,472,1295,2094,1987,1084,327,50,3,12,120,651,2096,4137,5032

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A102662; see the Formula section.

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

%F where u(1,x)=1, v(1,x)=1.  u=A207624; v=A102662.

%e First five rows:

%e 1

%e 2

%e 3...3

%e 4...8....3

%e 5...15...14...3

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

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

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

%t Table[Factor[u[n, x]], {n, 1, z}]

%t Table[Factor[v[n, x]], {n, 1, z}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%]    (* A207624 *)

%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[%]    (* A102662 *)

%Y Cf. A102662.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_, Feb 20 2012