cp's OEIS Frontend

A210190 Triangle of coefficients of polynomials v(n,x) jointly generated with A210189; see the Formula section.

%I A210190 #4 Mar 30 2012 18:58:16
%S A210190 1,2,2,3,8,4,20,4,5,40,24,6,70,84,8,7,112,224,64,8,168,504,288,16,9,
%T A210190 240,1008,960,160,10,330,1848,2640,880,32,11,440,3168,6336,3520,384,
%U A210190 12,572,5148,13728,11440,2496,64,13,728,8008,27456,32032,11648
%N A210190 Triangle of coefficients of polynomials v(n,x) jointly generated with A210189; see the Formula section.
%C A210190 For a discussion and guide to related arrays, see A208510.
%F A210190 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210190 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A210190 where u(1,x)=1, v(1,x)=1.
%e A210190 First five rows:
%e A210190 1
%e A210190 2...2
%e A210190 3...8
%e A210190 4...20...4
%e A210190 5...40...24
%e A210190 First three polynomials v(n,x): 1, 2 + 2x , 3 + 8x.
%t A210190 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210190 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210190 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210190 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210190 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210190 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210190 TableForm[cu]
%t A210190 Flatten[%]   (* A210189 *)
%t A210190 Table[Expand[v[n, x]], {n, 1, z}]
%t A210190 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210190 TableForm[cv]
%t A210190 Flatten[%]   (* A210190 *)
%Y A210190 Cf. A210189, A208510.
%K A210190 nonn,tabl
%O A210190 1,2
%A A210190 _Clark Kimberling_, Mar 18 2012