%I #4 Mar 30 2012 18:58:16
%S 1,3,6,2,11,7,2,19,19,9,2,32,44,30,11,2,53,94,83,43,13,2,87,190,207,
%T 137,58,15,2,142,370,480,387,208,75,17,2,231,701,1057,1004,653,298,94,
%U 19,2,375,1301,2238,2448,1865,1026,409,115,21,2,608,2376,4596
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210200; see the Formula section.
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 3
%e 6....2
%e 11...7....2
%e 19...19...9...2
%e First three polynomials u(n,x): 1, 3, 6 + 2x.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A210199 *)
%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[%] (* A210200 *)
%Y Cf. A210200, A208510.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Mar 18 2012