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A210189 Triangle of coefficients of polynomials u(n,x) jointly generated with A210190; see the Formula section.

%I A210189 #4 Mar 30 2012 18:58:16
%S A210189 1,3,6,2,10,10,15,30,4,21,70,28,28,140,112,8,36,252,336,72,45,420,840,
%T A210189 360,16,55,660,1848,1320,176,66,990,3696,3960,1056,32,78,1430,6864,
%U A210189 10296,4576,416,91,2002,12012,24024,16016,2912,64,105,2730,20020
%N A210189 Triangle of coefficients of polynomials u(n,x) jointly generated with A210190; see the Formula section.
%C A210189 Column 1:  triangular numbers: A000217
%C A210189 For a discussion and guide to related arrays, see A208510.
%F A210189 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210189 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A210189 where u(1,x)=1, v(1,x)=1.
%e A210189 First five rows:
%e A210189 1
%e A210189 3
%e A210189 6....2
%e A210189 10...10
%e A210189 15...30...4
%e A210189 First three polynomials u(n,x): 1, 3, 6 + 2x.
%t A210189 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210189 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210189 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210189 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210189 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210189 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210189 TableForm[cu]
%t A210189 Flatten[%]   (* A210189 *)
%t A210189 Table[Expand[v[n, x]], {n, 1, z}]
%t A210189 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210189 TableForm[cv]
%t A210189 Flatten[%]   (* A210190 *)
%Y A210189 Cf. A210190, A208510.
%K A210189 nonn,tabf
%O A210189 1,2
%A A210189 _Clark Kimberling_, Mar 18 2012