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%I #5 Mar 30 2012 18:58:15
%S 1,1,1,2,3,1,2,7,7,1,3,9,18,15,1,3,16,30,41,31,1,4,18,60,87,88,63,1,4,
%T 28,78,189,232,183,127,1,5,30,136,285,535,585,374,255,1,5,43,160,541,
%U 931,1410,1418,757,511,1,6,45,255,705,1886,2808,3534,3339,1524
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209558; 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)+2x*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 2...3...1
%e 2...7...7....1
%e 3...9...18...15...1
%e First three polynomials v(n,x): 1, 1 + x, 2 + 3x + 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] + 2 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[%] (* A209557 *)
%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[%] (* A209558 *)
%Y Cf. A209558, A208510.
%K nonn,tabl
%O 1,4
%A _Clark Kimberling_, Mar 10 2012
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