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%I #5 Mar 30 2012 18:58:15
%S 1,1,3,1,5,5,1,7,15,11,1,9,29,41,21,1,11,47,99,103,43,1,13,69,193,301,
%T 249,85,1,15,95,331,687,851,583,171,1,17,125,521,1349,2225,2285,1337,
%U 341,1,19,159,771,2391,4923,6735,5907,3015,683,1,21,197,1089
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209158; see the Formula section.
%C Alternating row sums: 1,-2,1,-2,1,-2,1,-2,1,-2,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...3
%e 1...5...5
%e 1...7...15...11
%e 1...9...29...41...21
%e First three polynomials v(n,x): 1, 1 + 3x, 1 + 5x + 5x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t v[n_, x_] := 2 x*u[n - 1, x] + 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[%] (* A209158 *)
%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[%] (* A209159 *)
%Y Cf. A209158, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 07 2012
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