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A210598 Triangle of coefficients of polynomials u(n,x) jointly generated with A210599; see the Formula section.

%I A210598 #5 Mar 30 2012 18:58:17
%S A210598 1,2,2,3,7,5,4,14,23,13,5,24,58,72,34,6,36,119,219,219,89,7,51,209,
%T A210598 521,777,653,233,8,68,338,1048,2101,2639,1918,610,9,88,508,1902,4754,
%U A210598 7989,8679,5567,1597,10,110,730,3180,9565,20055,29062,27844,16003
%N A210598 Triangle of coefficients of polynomials u(n,x) jointly generated with A210599; see the Formula section.
%C A210598 Row n starts with n and ends with an odd-indexed
%C A210598 Fibonacci number. For a discussion and guide to related
%C A210598 arrays, see A208510.
%F A210598 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A210598 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A210598 where u(1,x)=1, v(1,x)=1.
%e A210598 First five rows:
%e A210598 1
%e A210598 2...2
%e A210598 3...7....5
%e A210598 4...14...23...13
%e A210598 5...24...58...72...34
%e A210598 First three polynomials u(n,x): 1, 2+ 2x, 3 + 7x + 5x^2.
%t A210598 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210598 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210598 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210598 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210598 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210598 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210598 TableForm[cu]
%t A210598 Flatten[%]    (* A210598 *)
%t A210598 Table[Expand[v[n, x]], {n, 1, z}]
%t A210598 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210598 TableForm[cv]
%t A210598 Flatten[%]    (* A210599 *)
%Y A210598 Cf. A210599, A208510.
%K A210598 nonn,tabl
%O A210598 1,2
%A A210598 _Clark Kimberling_, Mar 24 2012