%I #4 Mar 30 2012 18:58:16
%S 1,3,1,7,4,1,15,12,5,1,31,32,18,6,1,63,80,56,25,7,1,127,192,160,88,33,
%T 8,1,255,448,432,280,129,42,9,1,511,1024,1120,832,450,180,52,10,1,
%U 1023,2304,2816,2352,1452,681,242,63,11,1,2047,5120,6912,6400
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210037; see the Formula section.
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F v(n,x)=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 3....1
%e 7....4....1
%e 15...12...5....1
%e 31...32...18...6...1
%e First three polynomials v(n,x): 1, 3 + x , 7 + 4x + x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%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[%] (* A210037 *)
%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[%] (* A210038 *)
%Y Cf. A210037, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 17 2012
|