%I #5 Mar 30 2012 18:58:16
%S 1,2,1,2,5,1,2,7,10,1,2,7,22,17,1,2,7,26,57,26,1,2,7,26,89,126,37,1,2,
%T 7,26,97,266,247,50,1,2,7,26,97,346,695,442,65,1,2,7,26,97,362,1127,
%U 1618,737,82,1,2,7,26,97,362,1319,3298,3425,1162,101,1,2,7,26
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210224; see the Formula section.
%C Limiting row: A001075
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F v(n,x)=2x*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...1
%e 2...5...1
%e 2...7...10...1
%e 2...7...22...17...1
%e First three polynomials u(n,x): 1, 2 + x, 2 + 5x + x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t v[n_, x_] := 2 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[%] (* A210223 *)
%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[%] (* A210224 *)
%Y Cf. A210224, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 20 2012
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