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%I #8 Apr 26 2016 12:07:07
%S 1,1,1,3,2,1,5,8,3,1,9,17,15,4,1,15,38,39,24,5,1,25,76,104,74,35,6,1,
%T 41,149,242,229,125,48,7,1,67,282,543,607,440,195,63,8,1,109,524,1159,
%U 1531,1308,769,287,80,9,1,177,957,2401,3631,3660,2533,1253,404
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209560; see the Formula section.
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,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 1...1
%e 3...2....1
%e 5...8....3....1
%e 9...17...15...4...1
%e First three polynomials v(n,x): 1, 1 + x, 3 + 2x + x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, 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[%] (* A209559 *)
%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[%] (* A209560 *)
%Y Cf. A209560, A208510.
%K nonn,tabl
%O 1,4
%A _Clark Kimberling_, Mar 10 2012
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