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%I #5 Mar 30 2012 18:58:14
%S 1,1,2,1,6,6,1,10,20,16,1,14,42,68,44,1,18,72,172,220,120,1,22,110,
%T 344,648,696,328,1,26,156,600,1480,2336,2160,896,1,30,210,956,2900,
%U 5984,8128,6608,2448,1,34,272,1428,5124,12984,23056,27536,19984
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208930; see the Formula section.
%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)+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 1...6...6
%e 1...10...20...16
%e 1...14...42...68...44
%e First five polynomials u(n,x):
%e 1
%e 1 + 2x
%e 1 + 6x + 6x^2
%e 1 + 10x + 20x^2 + 16x^3
%e 1 + 14x + 42x^2 + 68x^3 + 44x^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] + 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[%] (* A208909 *)
%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[%] (* A208930 *)
%Y Cf. A208909, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 04 2012
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