cp's OEIS Frontend

A210214 Triangle of coefficients of polynomials v(n,x) jointly generated with A210213; see the Formula section.

%I A210214 #4 Mar 30 2012 18:58:16
%S A210214 1,3,1,6,5,1,11,14,7,1,19,34,25,9,1,32,74,75,39,11,1,53,152,195,139,
%T A210214 56,13,1,87,299,468,419,231,76,15,1,142,571,1056,1147,791,356,99,17,1,
%U A210214 231,1066,2280,2911,2429,1364,519,125,19,1,375,1956,4755,6991
%N A210214 Triangle of coefficients of polynomials v(n,x) jointly generated with A210213; see the Formula section.
%C A210214 For a discussion and guide to related arrays, see A208510.
%F A210214 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210214 v(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210214 where u(1,x)=1, v(1,x)=1.
%e A210214 First five rows:
%e A210214 1
%e A210214 3....1
%e A210214 6....5....1
%e A210214 11...14...7....1
%e A210214 19...34...25...9...1
%e A210214 First three polynomials v(n,x): 1, 3 + x , 6 + 5x + x^2.
%t A210214 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210214 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210214 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210214 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210214 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210214 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210214 TableForm[cu]
%t A210214 Flatten[%]    (* A210213 *)
%t A210214 Table[Expand[v[n, x]], {n, 1, z}]
%t A210214 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210214 TableForm[cv]
%t A210214 Flatten[%]    (* A210214 *)
%Y A210214 Cf. A210213, A208510.
%K A210214 nonn,tabl
%O A210214 1,2
%A A210214 _Clark Kimberling_, Mar 19 2012