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%I #5 Mar 30 2012 18:58:13
%S 1,1,1,1,2,4,1,3,8,10,1,4,12,22,28,1,5,16,36,68,76,1,6,20,52,120,200,
%T 208,1,7,24,70,184,376,592,568,1,8,28,90,260,608,1184,1736,1552,1,9,
%U 32,112,348,900,2016,3672,5072,4240,1,10,36,136,448,1256,3120
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208527; see the Formula section.
%F u(n,x)=u(n-1,x)+x*v(n-1,x),
%F v(n,x)=2x*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...1
%e 1...2...4
%e 1...3...8....10
%e 1...4...12...22...28
%e First five polynomials u(n,x):
%e 1
%e 1 + x
%e 1 + 2x + 4x^2
%e 1 + 3x + 8x^2 + 10x^3
%e 1 + 4x + 12x^2 + 22x^3 + 28x^4
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t v[n_, x_] := 2 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[%] (* A208526 *)
%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[%] (* A208527 *)
%Y Cf. A208527.
%K nonn,tabl
%O 1,5
%A _Clark Kimberling_, Feb 29 2012
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