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%I #6 Mar 30 2012 18:58:15
%S 1,1,2,3,5,3,5,14,12,4,9,30,40,23,5,15,63,107,93,39,6,25,124,264,300,
%T 190,61,7,41,238,604,858,722,354,90,8,67,445,1319,2242,2364,1559,615,
%U 127,9,109,818,2772,5500,6966,5783,3101,1011,173,10,177,1482
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209754; 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)+(x+1)*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 3...5....3
%e 5...14...12...4
%e 9...30...40...23...5
%e First three polynomials u(n,x): 1, 1 + 2x, 3 + 5x + 3x^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] + (x + 1)*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[%] (* A209753 *)
%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[%] (* A209754 *)
%Y Cf. A209754, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 14 2012
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