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A210230 Triangle of coefficients of polynomials v(n,x) jointly generated with A210229; see the Formula section.

%I A210230 #4 Mar 30 2012 18:58:16
%S A210230 1,3,1,6,4,1,11,11,5,1,19,26,17,6,1,32,56,48,24,7,1,53,114,121,78,32,
%T A210230 8,1,87,223,283,223,117,41,9,1,142,424,627,584,372,166,51,10,1,231,
%U A210230 789,1334,1434,1073,579,226,62,11,1,375,1444,2750,3352,2879,1818
%N A210230 Triangle of coefficients of polynomials v(n,x) jointly generated with A210229; see the Formula section.
%C A210230 Alternating row sums: 1,2,3,4,5,6,... (A000027)
%C A210230 For a discussion and guide to related arrays, see A208510.
%F A210230 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210230 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A210230 where u(1,x)=1, v(1,x)=1.
%e A210230 First five rows:
%e A210230 1
%e A210230 3....1
%e A210230 6....4....1
%e A210230 11...11...5....1
%e A210230 19...26...17...6...1
%e A210230 First three polynomials v(n,x): 1, 3 + x , 6 + 4x + x^2.
%t A210230 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210230 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210230 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A210230 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210230 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210230 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210230 TableForm[cu]
%t A210230 Flatten[%]     (* A210229 *)
%t A210230 Table[Expand[v[n, x]], {n, 1, z}]
%t A210230 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210230 TableForm[cv]
%t A210230 Flatten[%]     (* A210230 *)
%Y A210230 Cf. A210229, A208510.
%K A210230 nonn,tabl
%O A210230 1,2
%A A210230 _Clark Kimberling_, Mar 20 2012