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A210231 Triangle of coefficients of polynomials u(n,x) jointly generated with A210232; see the Formula section.

%I A210231 #4 Mar 30 2012 18:58:16
%S A210231 1,2,1,3,4,1,4,8,7,1,5,14,18,11,1,6,21,39,36,16,1,7,30,69,93,66,22,1,
%T A210231 8,40,114,192,199,113,29,1,9,52,172,360,474,393,183,37,1,10,65,250,
%U A210231 610,997,1068,729,283,46,1,11,80,345,980,1882,2501,2238,1285,421
%N A210231 Triangle of coefficients of polynomials u(n,x) jointly generated with A210232; see the Formula section.
%C A210231 For a discussion and guide to related arrays, see A208510.
%F A210231 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210231 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A210231 where u(1,x)=1, v(1,x)=1.
%e A210231 First five rows:
%e A210231 1
%e A210231 2...1
%e A210231 3...4....1
%e A210231 4...8....7....1
%e A210231 5...14...18...11...1
%e A210231 First three polynomials u(n,x): 1, 2 + x, 3 + 4x + x^2.
%t A210231 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210231 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210231 v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210231 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210231 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210231 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210231 TableForm[cu]
%t A210231 Flatten[%]     (* A210231 *)
%t A210231 Table[Expand[v[n, x]], {n, 1, z}]
%t A210231 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210231 TableForm[cv]
%t A210231 Flatten[%]     (* A210232 *)
%Y A210231 Cf. A210232, A208510.
%K A210231 nonn,tabl
%O A210231 1,2
%A A210231 _Clark Kimberling_, Mar 20 2012