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A210192 Triangle of coefficients of polynomials v(n,x) jointly generated with A210191; see the Formula section.

%I A210192 #4 Mar 30 2012 18:58:16
%S A210192 1,1,3,1,7,3,1,11,13,3,1,15,31,19,3,1,19,57,63,25,3,1,23,91,151,107,
%T A210192 31,3,1,27,133,299,321,163,37,3,1,31,183,523,771,591,231,43,3,1,35,
%U A210192 241,839,1593,1683,985,311,49,3,1,39,307,1263,2955,4047,3259,1527
%N A210192 Triangle of coefficients of polynomials v(n,x) jointly generated with A210191; see the Formula section.
%C A210192 For a discussion and guide to related arrays, see A208510.
%F A210192 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210192 v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F A210192 where u(1,x)=1, v(1,x)=1.
%e A210192 First five rows:
%e A210192 1
%e A210192 1...3
%e A210192 1...7....3
%e A210192 1...11...13...3
%e A210192 1...15...31...19...3
%e A210192 First three polynomials v(n,x): 1, 1 + 3x , 1 + 7x + 3x^2.
%t A210192 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210192 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210192 v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210192 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210192 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210192 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210192 TableForm[cu]
%t A210192 Flatten[%]   (* A210191 *)
%t A210192 Table[Expand[v[n, x]], {n, 1, z}]
%t A210192 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210192 TableForm[cv]
%t A210192 Flatten[%]   (* A210192 *)
%Y A210192 Cf. A210191, A208510.
%K A210192 nonn,tabl
%O A210192 1,3
%A A210192 _Clark Kimberling_, Mar 18 2012