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