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A210223 Triangle of coefficients of polynomials u(n,x) jointly generated with A210224; see the Formula section.

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