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A210227 Triangle of coefficients of polynomials u(n,x) jointly generated with A210228; see the Formula section.

%I A210227 #4 Mar 30 2012 18:58:16
%S A210227 1,2,1,2,6,1,2,8,16,1,2,8,32,38,1,2,8,36,112,84,1,2,8,36,156,348,178,
%T A210227 1,2,8,36,164,620,988,368,1,2,8,36,164,732,2244,2624,750,1,2,8,36,164,
%U A210227 748,3108,7468,6632,1516,1,2,8,36,164,748,3380,12348,23164
%N A210227 Triangle of coefficients of polynomials u(n,x) jointly generated with A210228; see the Formula section.
%C A210227 For a discussion and guide to related arrays, see A208510.
%F A210227 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210227 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A210227 where u(1,x)=1, v(1,x)=1.
%e A210227 First five rows:
%e A210227 1
%e A210227 2...1
%e A210227 2...6...1
%e A210227 2...8...16...1
%e A210227 2...8...32...38...1
%e A210227 First three polynomials u(n,x): 1, 2 + x, 2 + 6x + x^2.
%t A210227 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210227 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210227 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210227 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210227 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210227 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210227 TableForm[cu]
%t A210227 Flatten[%]     (* A210225 *)
%t A210227 Table[Expand[v[n, x]], {n, 1, z}]
%t A210227 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210227 TableForm[cv]
%t A210227 Flatten[%]     (* A210226 *)
%Y A210227 Cf. A210228, A208510.
%K A210227 nonn,tabl
%O A210227 1,2
%A A210227 _Clark Kimberling_, Mar 20 2012