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A210203 Triangle of coefficients of polynomials u(n,x) jointly generated with A210204; see the Formula section.

%I A210203 #5 Mar 30 2012 18:58:16
%S A210203 1,3,7,2,15,10,2,31,34,14,2,63,98,62,18,2,127,258,222,98,22,2,255,642,
%T A210203 702,418,142,26,2,511,1538,2046,1538,702,194,30,2,1023,3586,5630,5122,
%U A210203 2942,1090,254,34,2,2047,8194,14846,15874,11006,5122,1598,322
%N A210203 Triangle of coefficients of polynomials u(n,x) jointly generated with A210204; see the Formula section.
%C A210203 Column 1: -1+2^n
%C A210203 Row sums: 3^(n-1)
%C A210203 Alternating row sums: 1,1,1,1,1,1,1,1,1,...
%C A210203 For a discussion and guide to related arrays, see A208510.
%F A210203 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210203 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210203 where u(1,x)=1, v(1,x)=1.
%e A210203 First five rows:
%e A210203 1
%e A210203 3
%e A210203 7....2
%e A210203 15...10...2
%e A210203 31...34...14...2
%e A210203 First three polynomials u(n,x): 1, 3, 7 + 2x.
%t A210203 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210203 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210203 v[n_, x_] := (x+1)*u[n-1,x]+(x+1)*v[n-1,x]+1;
%t A210203 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210203 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210203 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210203 TableForm[cu]
%t A210203 Flatten[%]   (* A210203 *)
%t A210203 Table[Expand[v[n, x]], {n, 1, z}]
%t A210203 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210203 TableForm[cv]
%t A210203 Flatten[%]   (* A210204 *)
%Y A210203 Cf. A210204, A208510.
%K A210203 nonn,tabf
%O A210203 1,2
%A A210203 _Clark Kimberling_, Mar 18 2012