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A208916 Triangle of coefficients of polynomials v(n,x) jointly generated with A208915; see the Formula section.

%I A208916 #5 Mar 30 2012 18:58:14
%S A208916 1,1,3,1,3,7,1,3,11,19,1,3,15,35,47,1,3,19,51,107,123,1,3,23,67,183,
%T A208916 323,311,1,3,27,83,275,603,939,803,1,3,31,99,383,963,1951,2723,2047,1,
%U A208916 3,35,115,507,1403,3411,6147,7723,5259,1,3,39,131,647,1923,5383
%N A208916 Triangle of coefficients of polynomials v(n,x) jointly generated with A208915; see the Formula section.
%C A208916 For a discussion and guide to related arrays, see A208510.
%F A208916 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208916 v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F A208916 where u(1,x)=1, v(1,x)=1.
%e A208916 First five rows:
%e A208916 1
%e A208916 1...3
%e A208916 1...3...7
%e A208916 1...3...11...19
%e A208916 1...3...15...35...47
%e A208916 First five polynomials v(n,x):
%e A208916 1
%e A208916 1 + 3x
%e A208916 1 + 3x + 7x^2
%e A208916 1 + 3x + 11x^2 + 19x^3
%e A208916 1 + 3x + 15x^2 + 35x^3 + 47x^4
%t A208916 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208916 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208916 v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A208916 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208916 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208916 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208916 TableForm[cu]
%t A208916 Flatten[%]    (* A208915 *)
%t A208916 Table[Expand[v[n, x]], {n, 1, z}]
%t A208916 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208916 TableForm[cv]
%t A208916 Flatten[%]    (* A208916 *)
%Y A208916 Cf. A208915, A208510.
%K A208916 nonn,tabl
%O A208916 1,3
%A A208916 _Clark Kimberling_, Mar 03 2012