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%I #5 Mar 30 2012 18:58:14
%S 1,3,2,5,8,4,7,22,24,8,9,48,84,60,16,11,90,228,264,148,32,13,152,528,
%T 876,772,348,64,15,238,1092,2424,2992,2112,804,128,17,352,2072,5896,
%U 9568,9392,5548,1820,256,19,498,3672,13008,26648,34080,27780
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208932; see the Formula section.
%C Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F v(n,x)=(x+1)*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 3...2
%e 5...8....4
%e 7...22...24...8
%e 9...48...84...60...16
%e First five polynomials v(n,x):
%e 1
%e 3 + 2x
%e 5 + 8x + 4x^2
%e 7 + 22x + 24x^2 + 8x^3
%e 9 + 48x + 84x^2 + 60x^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 + 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[%] (* A208931 *)
%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[%] (* A208932 *)
%Y Cf. A208930, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 04 2012
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