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A210033 Triangle of coefficients of polynomials u(n,x) jointly generated with A210034; see the Formula section.

%I A210033 #5 Mar 30 2012 18:58:16
%S A210033 1,3,6,1,11,3,1,19,8,3,1,32,18,9,3,1,53,38,22,10,3,1,87,76,51,26,11,3,
%T A210033 1,142,147,111,65,30,12,3,1,231,277,233,151,80,34,13,3,1,375,512,474,
%U A210033 338,196,96,38,14,3,1,608,932,942,730,463,246,113,42,15,3,1
%N A210033 Triangle of coefficients of polynomials u(n,x) jointly generated with A210034; see the Formula section.
%C A210033 For a discussion and guide to related arrays, see A208510.
%F A210033 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210033 v(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F A210033 where u(1,x)=1, v(1,x)=1.
%e A210033 First five rows:
%e A210033 1
%e A210033 3
%e A210033 6....1
%e A210033 11...3...1
%e A210033 19...8...3...1
%e A210033 First three polynomials u(n,x): 1, 3, 6 + x.
%t A210033 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210033 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210033 v[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210033 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210033 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210033 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210033 TableForm[cu]
%t A210033 Flatten[%]    (* A210033 *)
%t A210033 Table[Expand[v[n, x]], {n, 1, z}]
%t A210033 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210033 TableForm[cv]
%t A210033 Flatten[%]    (* A210034 *)
%Y A210033 Cf. A210034, A208510.
%K A210033 nonn,tabf
%O A210033 1,2
%A A210033 _Clark Kimberling_, Mar 16 2012