A207625 - OEIS

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

%S 1,2,4,3,7,12,3,11,32,21,3,16,70,83,30,3,22,135,247,161,39,3,29,238,

%T 616,622,266,48,3,37,392,1358,1946,1276,398,57,3,46,612,2730,5244,

%U 4854,2290,557,66,3,56,915,5106,12630,15622,10312,3745,743,75,3,67

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A207626; see the Formula section.

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

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

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

%e First five rows:

%e 1

%e 2

%e 4....3

%e 7....12...3

%e 11...32...21...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 + 1)*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[%]    (* A207625 *)

%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[%]    (* A207626 *)

%Y Cf. A207626.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_, Feb 21 2012