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Triangle of coefficients of polynomials u(n,x) jointly generated with A209147; see the Formula section.
4

%I #5 Mar 30 2012 18:58:15

%S 1,2,1,4,5,2,7,13,11,4,12,29,34,24,8,20,60,90,85,52,16,33,118,215,255,

%T 206,112,32,54,225,481,680,683,488,240,64,88,419,1028,1682,1994,1760,

%U 1136,512,128,143,767,2122,3937,5361,5553,4408,2608,1088,256

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209147; see the Formula section.

%C Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,...

%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)=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 2...1

%e 4...5...2

%e 7...13...11...4

%e 12...29...34...24...8

%e First three polynomials v(n,x): 1, 2 + x, 4 + 5x + 2x^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_] := 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[%] (* A209146 *)

%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[%] (* A209147 *)

%Y Cf. A209146, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 06 2012