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%I #5 Mar 30 2012 18:58:14
%S 1,2,2,2,5,4,2,9,15,8,2,13,33,37,16,2,17,59,103,91,32,2,21,93,221,297,
%T 213,64,2,25,135,407,739,807,491,128,2,29,185,677,1553,2285,2105,1109,
%U 256,2,33,243,1047,2907,5391,6675,5319,2475,512,2,37,309,1533
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208923; see the Formula section.
%C Alternating row sums: 1,0,1,0,1,0,1,0,1,0,1,0,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F v(n,x)=(x+1)*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 2...2
%e 2...5....4
%e 2...9...15...8
%e 2...13...33...37...16
%e First five polynomials v(n,x):
%e 1
%e 2 + 2x
%e 2 + 5x + 4x^2
%e 2 + 9x + 15x^2 + 8x^3
%e 2 + 13x + 33x^2 + 37x^3 + 16x^4
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t v[n_, x_] := (x + 1)*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[%] (* A208923 *)
%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[%] (* A208908 *)
%Y Cf. A208923, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 04 2012
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