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

%I A209576 #6 Mar 30 2012 18:58:15
%S A209576 1,1,4,1,4,10,1,4,18,22,1,4,18,66,46,1,4,18,82,206,94,1,4,18,82,342,
%T A209576 578,190,1,4,18,82,374,1274,1510,382,1,4,18,82,374,1642,4294,3754,766,
%U A209576 1,4,18,82,374,1706,6726,13354,9006,1534,1,4,18,82,374,1706
%N A209576 Triangle of coefficients of polynomials v(n,x) jointly generated with A209575; see the Formula section.
%C A209576 For a discussion and guide to related arrays, see A208510.
%F A209576 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209576 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A209576 where u(1,x)=1, v(1,x)=1.
%e A209576 First five rows:
%e A209576 1
%e A209576 1...4
%e A209576 1...4...10
%e A209576 1...4...18...22
%e A209576 1...4...18...66...46
%e A209576 First three polynomials v(n,x): 1, 1+4x, 1+4x+10x^2.
%t A209576 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209576 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209576 v[n_, x_] := 2 x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209576 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209576 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209576 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209576 TableForm[cu]
%t A209576 Flatten[%]   (* A209575 *)
%t A209576 Table[Expand[v[n, x]], {n, 1, z}]
%t A209576 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209576 TableForm[cv]
%t A209576 Flatten[%]   (* A209576 *)
%Y A209576 Cf. A209575, A208510.
%K A209576 nonn,tabl
%O A209576 1,3
%A A209576 _Clark Kimberling_, Mar 11 2012