%I #6 Mar 30 2012 18:58:15
%S 1,1,2,2,5,4,2,10,15,8,3,14,35,39,16,3,22,63,108,95,32,4,27,109,235,
%T 309,223,64,4,38,160,454,782,838,511,128,5,44,242,770,1688,2408,2183,
%U 1151,256,5,58,322,1264,3226,5776,7009,5512,2559,512,6,65,450
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209752; see the Formula section.
%C Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=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 1...2
%e 2...5....4
%e 2...10...15...8
%e 3...14...35...39...16
%e First three polynomials u(n,x): 1, 1 + 2x, 2 + 5x + 4x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := 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[%] (* A209751 *)
%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[%] (* A209752 *)
%Y Cf. A209752, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 14 2012
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