cp's OEIS Frontend

A209698 Triangle of coefficients of polynomials v(n,x) jointly generated with A209697; see the Formula section.

%I A209698 #5 Mar 30 2012 18:58:15
%S A209698 1,2,2,3,4,4,4,7,10,8,5,11,20,24,16,6,16,35,54,56,32,7,22,56,104,140,
%T A209698 128,64,8,29,84,181,294,352,288,128,9,37,120,293,552,800,864,640,256,
%U A209698 10,46,165,449,957,1610,2112,2080,1408,512,11,56,220,659,1562
%N A209698 Triangle of coefficients of polynomials v(n,x) jointly generated with A209697; see the Formula section.
%C A209698 For a discussion and guide to related arrays, see A208510.
%F A209698 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209698 v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209698 where u(1,x)=1, v(1,x)=1.
%e A209698 First five rows:
%e A209698 1
%e A209698 2...2
%e A209698 3...4....4
%e A209698 4...7....10...8
%e A209698 5...11...20...24...16
%e A209698 First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 4x^2.
%t A209698 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209698 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t A209698 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209698 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209698 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209698 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209698 TableForm[cu]
%t A209698 Flatten[%]   (* A209697 *)
%t A209698 Table[Expand[v[n, x]], {n, 1, z}]
%t A209698 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209698 TableForm[cv]
%t A209698 Flatten[%]   (* A209698 *)
%Y A209698 Cf. A209697, A208510.
%K A209698 nonn,tabl
%O A209698 1,2
%A A209698 _Clark Kimberling_, Mar 12 2012