%I #6 Mar 30 2012 18:58:15
%S 1,0,2,0,3,3,0,4,9,4,0,5,17,19,5,0,6,27,49,34,6,0,7,39,98,115,55,7,0,
%T 8,53,170,284,236,83,8,0,9,69,269,585,706,440,119,9,0,10,87,399,1070,
%U 1706,1568,763,164,10,0,11,107,564,1799,3577,4395,3193,1250,219
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209694; see the Formula section.
%C Alternating row sums are periodic.
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F v(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 0...2
%e 0...2...4
%e 0...1...8...8
%e 0...1...5...24...16
%e First three polynomials v(n,x): 1, 2x, 2x + 4x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t v[n_, x_] := u[n - 1, x] + (x + 1)*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[%] (* A209693 *)
%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[%] (* A209694 *)
%Y Cf. A209694, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 12 2012