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A210225 Triangle of coefficients of polynomials u(n,x) jointly generated with A210226; see the Formula section.

%I A210225 #4 Mar 30 2012 18:58:16
%S A210225 1,2,1,3,5,1,4,12,10,1,5,22,36,17,1,6,35,88,87,26,1,7,51,175,277,181,
%T A210225 37,1,8,70,306,680,734,338,50,1,9,92,490,1416,2196,1710,582,65,1,10,
%U A210225 117,736,2632,5402,6156,3606,941,82,1,11,145,1053,4502,11592
%N A210225 Triangle of coefficients of polynomials u(n,x) jointly generated with A210226; see the Formula section.
%C A210225 For a discussion and guide to related arrays, see A208510.
%F A210225 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210225 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210225 where u(1,x)=1, v(1,x)=1.
%e A210225 First five rows:
%e A210225 1
%e A210225 2...1
%e A210225 3...5....1
%e A210225 4...12...10...1
%e A210225 5...22...36...17...1
%e A210225 First three polynomials u(n,x): 1, 2 + x, 3 + 5x + x^2.
%t A210225 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210225 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210225 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210225 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210225 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210225 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210225 TableForm[cu]
%t A210225 Flatten[%]     (* A210225 *)
%t A210225 Table[Expand[v[n, x]], {n, 1, z}]
%t A210225 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210225 TableForm[cv]
%t A210225 Flatten[%]     (* A210226 *)
%Y A210225 Cf. A210226, A208510.
%K A210225 nonn,tabl
%O A210225 1,2
%A A210225 _Clark Kimberling_, Mar 20 2012