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A210738 Triangle of coefficients of polynomials v(n,x) jointly generated with A210603; see the Formula section.

%I A210738 #6 Mar 30 2012 18:58:17
%S A210738 1,3,2,6,9,4,11,25,23,8,19,60,81,55,16,32,130,237,233,127,32,53,266,
%T A210738 610,798,625,287,64,87,522,1451,2364,2439,1601,639,128,142,995,3255,
%U A210738 6373,8138,6984,3969,1407,256,231,1855,6995,16007,24430,25832
%N A210738 Triangle of coefficients of polynomials v(n,x) jointly generated with A210603; see the Formula section.
%C A210738 Row n starts with F(n+3)-2, where F=A000045 (Fibonacci
%C A210738 numbers), and ends with 2^(n-1). For a discussion and
%C A210738 guide to related arrays, see A208510.
%F A210738 u(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A210738 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210738 where u(1,x)=1, v(1,x)=1.
%e A210738 First five rows:
%e A210738 1
%e A210738 3....2
%e A210738 6....9....4
%e A210738 11...25...23...8
%e A210738 19...60...81...55...16
%e A210738 First three polynomials v(n,x): 1, 3 + 2x, 6 + 9x + 4x^2
%t A210738 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210738 u[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210738 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210738 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210738 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210738 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210738 TableForm[cu]
%t A210738 Flatten[%]    (* A210603 *)
%t A210738 Table[Expand[v[n, x]], {n, 1, z}]
%t A210738 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210738 TableForm[cv]
%t A210738 Flatten[%]    (* A210738 *)
%Y A210738 Cf. A210603, A208510.
%K A210738 nonn,tabl
%O A210738 1,2
%A A210738 _Clark Kimberling_, Mar 24 2012