%I #5 Mar 30 2012 18:58:16
%S 1,1,2,1,4,3,1,6,8,5,1,8,15,17,8,1,10,24,38,33,13,1,12,35,70,86,63,21,
%T 1,14,48,115,180,187,117,34,1,16,63,175,330,437,390,214,55,1,18,80,
%U 252,553,882,1007,791,386,89,1,20,99,348,868,1610,2219,2235,1567
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210560; see the Formula section.
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...2
%e 1...4...3
%e 1...6...8....5
%e 1...8...15...17...8
%e First three polynomials u(n,x): 1, 1 + 2x, 1 + 4x + 3x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A210559 *)
%t Table[Expand[v[n, x]], {n, 1, z}]
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210560 *)
%Y Cf. A210560, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 22 2012