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A209575 Triangle of coefficients of polynomials u(n,x) jointly generated with A209576; see the Formula section.

%I A209575 #5 Mar 30 2012 18:58:15
%S A209575 1,1,1,1,5,1,1,5,15,1,1,5,23,37,1,1,5,23,89,83,1,1,5,23,105,295,177,1,
%T A209575 1,5,23,105,447,873,367,1,1,5,23,105,479,1721,2383,749,1,1,5,23,105,
%U A209575 479,2121,6015,6137,1515,1,1,5,23,105,479,2185,8847,19369,15143
%N A209575 Triangle of coefficients of polynomials u(n,x) jointly generated with A209576; see the Formula section.
%C A209575 For a discussion and guide to related arrays, see A208510.
%F A209575 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209575 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A209575 where u(1,x)=1, v(1,x)=1.
%e A209575 First five rows:
%e A209575 1
%e A209575 1...1
%e A209575 1...5...1
%e A209575 1...5...15...1
%e A209575 1...5...23...37...1
%e A209575 First three polynomials v(n,x): 1, 1 + x, 1 + 5x + x^2.
%t A209575 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209575 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209575 v[n_, x_] := 2 x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209575 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209575 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209575 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209575 TableForm[cu]
%t A209575 Flatten[%]   (* A209575 *)
%t A209575 Table[Expand[v[n, x]], {n, 1, z}]
%t A209575 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209575 TableForm[cv]
%t A209575 Flatten[%]   (* A209576 *)
%Y A209575 Cf. A209576, A208510.
%K A209575 nonn,tabl
%O A209575 1,5
%A A209575 _Clark Kimberling_, Mar 11 2012