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%I #4 Mar 30 2012 18:58:16
%S 1,3,6,2,10,10,15,30,4,21,70,28,28,140,112,8,36,252,336,72,45,420,840,
%T 360,16,55,660,1848,1320,176,66,990,3696,3960,1056,32,78,1430,6864,
%U 10296,4576,416,91,2002,12012,24024,16016,2912,64,105,2730,20020
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210190; see the Formula section.
%C Column 1: triangular numbers: A000217
%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)=2x*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 3
%e 6....2
%e 10...10
%e 15...30...4
%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_] := 2 x*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[%] (* A210189 *)
%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[%] (* A210190 *)
%Y Cf. A210190, A208510.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Mar 18 2012