|
%I #5 Mar 30 2012 18:58:15
%S 1,3,1,5,5,1,9,12,7,1,15,29,22,9,1,25,61,66,35,11,1,41,124,166,125,51,
%T 13,1,67,241,394,365,211,70,15,1,109,457,877,988,701,329,92,17,1,177,
%U 848,1877,2472,2129,1225,484,117,19,1,287,1549,3884,5880,5909
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209559; see the Formula section.
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+v(n-1,x),
%F v(n,x)=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 3....1
%e 5....5....1
%e 9....12...7....1
%e 15...29...22...9...1
%e First three polynomials v(n,x): 1, 3 + x , 5 + 5x + x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t v[n_, x_] := u[n - 1, x] + (x + 1)*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[%] (* A209559 *)
%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[%] (* A209560 *)
%Y Cf. A209559, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 10 2012
|
