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%I #5 Mar 30 2012 18:58:13
%S 1,1,2,1,2,3,1,2,4,5,1,2,5,8,8,1,2,6,11,15,13,1,2,7,14,23,28,21,1,2,8,
%T 17,32,47,51,34,1,2,9,20,42,70,93,92,55,1,2,10,23,53,97,148,181,164,
%U 89,1,2,11,26,65,128,217,306,346,290,144,1,2,12,29,78,163,301
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208514; see the Formula section.
%F u(n,x)=u(n-1,x)+x*v(n-1,x),
%F v(n,x)=x*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 1...2
%e 1...2...3
%e 1...2...4...5
%e 1...2...5...8...8
%e First five polynomials v(n,x):
%e 1
%e 1 + 2x
%e 1 + 2x + 3x^2
%e 1 + 2x + 4x^2 + 5x^3
%e 1 + 2x + 5x^2 + 8x^3 + 8x^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_] := x*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[%] (* A208514 *)
%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[%] (* A208515 *)
%Y Cf. A208514.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Feb 28 2012
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