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A210232 Triangle of coefficients of polynomials v(n,x) jointly generated with A210231; see the Formula section.

%I A210232 #4 Mar 30 2012 18:58:16
%S A210232 1,2,2,3,5,3,4,10,10,4,5,16,25,18,5,6,24,48,54,30,6,7,33,84,123,106,
%T A210232 47,7,8,44,132,246,282,194,70,8,9,56,198,438,637,594,336,100,9,10,70,
%U A210232 280,730,1272,1504,1170,556,138,10,11,85,385,1140,2337,3337,3301
%N A210232 Triangle of coefficients of polynomials v(n,x) jointly generated with A210231; see the Formula section.
%C A210232 First and last terms of row n are n.
%C A210232 Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...
%C A210232 For a discussion and guide to related arrays, see A208510.
%F A210232 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210232 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A210232 where u(1,x)=1, v(1,x)=1.
%e A210232 First five rows:
%e A210232 1
%e A210232 2...2
%e A210232 3...5....3
%e A210232 4...10...10...4
%e A210232 5...16...25...16...5
%e A210232 First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 3x^2.
%t A210232 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210232 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210232 v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210232 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210232 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210232 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210232 TableForm[cu]
%t A210232 Flatten[%]     (* A210231 *)
%t A210232 Table[Expand[v[n, x]], {n, 1, z}]
%t A210232 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210232 TableForm[cv]
%t A210232 Flatten[%]     (* A210232 *)
%Y A210232 Cf. A210231, A208510.
%K A210232 nonn,tabl
%O A210232 1,2
%A A210232 _Clark Kimberling_, Mar 20 2012