cp's OEIS Frontend

A210224 Triangle of coefficients of polynomials v(n,x) jointly generated with A210223; see the Formula section.

%I A210224 #4 Mar 30 2012 18:58:16
%S A210224 1,1,3,1,5,5,1,5,15,7,1,5,19,35,9,1,5,19,63,69,11,1,5,19,71,177,121,
%T A210224 13,1,5,19,71,249,429,195,15,1,5,19,71,265,781,923,295,17,1,5,19,71,
%U A210224 265,957,2171,1807,425,19,1,5,19,71,265,989,3211,5407,3281,589,21
%N A210224 Triangle of coefficients of polynomials v(n,x) jointly generated with A210223; see the Formula section.
%C A210224 Limiting row:  A001834
%C A210224 For a discussion and guide to related arrays, see A208510.
%F A210224 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210224 v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F A210224 where u(1,x)=1, v(1,x)=1.
%e A210224 First five rows:
%e A210224 1
%e A210224 1...3
%e A210224 1...5...5
%e A210224 1...5...15...7
%e A210224 1...5...19...35...9
%e A210224 First three polynomials v(n,x): 1, 1 + 3x , 1 + 5x + 5x^2.
%t A210224 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210224 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210224 v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210224 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210224 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210224 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210224 TableForm[cu]
%t A210224 Flatten[%]     (* A210223 *)
%t A210224 Table[Expand[v[n, x]], {n, 1, z}]
%t A210224 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210224 TableForm[cv]
%t A210224 Flatten[%]     (* A210224 *)
%Y A210224 Cf. A210223, A208510.
%K A210224 nonn,tabl
%O A210224 1,3
%A A210224 _Clark Kimberling_, Mar 20 2012