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A210233 Triangle of coefficients of polynomials u(n,x) jointly generated with A210234; see the Formula section.

%I A210233 #4 Mar 30 2012 18:58:16
%S A210233 1,2,1,3,5,1,4,10,12,1,5,18,30,27,1,6,27,68,83,58,1,7,39,119,225,217,
%T A210233 121,1,8,52,200,454,680,544,248,1,9,68,300,866,1566,1928,1320,503,1,
%U A210233 10,85,440,1450,3332,5014,5216,3121,1014,1,11,105,605,2350,6182
%N A210233 Triangle of coefficients of polynomials u(n,x) jointly generated with A210234; see the Formula section.
%C A210233 For a discussion and guide to related arrays, see A208510.
%F A210233 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210233 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A210233 where u(1,x)=1, v(1,x)=1.
%e A210233 First five rows:
%e A210233 1
%e A210233 2...1
%e A210233 3...5....1
%e A210233 4...10...12...1
%e A210233 5...18...30...27...1
%e A210233 First three polynomials u(n,x): 1, 2 + x, 3 + 5x + x^2.
%t A210233 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210233 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210233 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210233 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210233 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210233 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210233 TableForm[cu]
%t A210233 Flatten[%]      (* A210233 *)
%t A210233 Table[Expand[v[n, x]], {n, 1, z}]
%t A210233 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210233 TableForm[cv]
%t A210233 Flatten[%]      (* A210234 *)
%Y A210233 Cf. A210234, A208510.
%K A210233 nonn,tabl
%O A210233 1,2
%A A210233 _Clark Kimberling_, Mar 20 2012