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A209558 Triangle of coefficients of polynomials v(n,x) jointly generated with A209557; see the Formula section.

%I A209558 #5 Mar 30 2012 18:58:15
%S A209558 1,2,2,2,5,4,3,7,11,8,3,13,21,23,16,4,15,44,57,47,32,4,24,60,129,145,
%T A209558 95,64,5,26,108,207,346,353,191,128,5,38,130,405,646,875,833,383,256,
%U A209558 6,40,212,545,1345,1877,2124,1921,767,512,6,55,240,965,2021
%N A209558 Triangle of coefficients of polynomials v(n,x) jointly generated with A209557; see the Formula section.
%C A209558 For a discussion and guide to related arrays, see A208510.
%F A209558 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209558 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A209558 where u(1,x)=1, v(1,x)=1.
%e A209558 First five rows:
%e A209558 1
%e A209558 2...2
%e A209558 2...5...4
%e A209558 3...7...11...8
%e A209558 3...13...21...23...16
%e A209558 First three polynomials v(n,x): 1, 2 + 2x , 2+ 5x + 4x^2 .
%t A209558 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209558 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209558 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209558 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209558 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209558 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209558 TableForm[cu]
%t A209558 Flatten[%]    (* A209557 *)
%t A209558 Table[Expand[v[n, x]], {n, 1, z}]
%t A209558 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209558 TableForm[cv]
%t A209558 Flatten[%]    (* A209558 *)
%Y A209558 Cf. A209557, A208510.
%K A209558 nonn,tabl
%O A209558 1,2
%A A209558 _Clark Kimberling_, Mar 10 2012