%I #5 Mar 30 2012 18:58:17

%S 1,3,1,6,7,1,11,21,15,1,19,53,60,31,1,32,118,191,155,63,1,53,246,514,

%T 593,378,127,1,87,489,1261,1863,1683,889,255,1,142,941,2890,5233,6029,

%U 4501,2040,511,1,231,1767,6311,13527,19026,18068,11543,4599

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210750; see the Formula section.

%C Row n starts with -2+F(n+3) and ends with 1, where F=A000045 (Fibonacci numbers).

%C For a discussion and guide to related arrays, see A208510.

%F u(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,

%F v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,

%F where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 3....1

%e 6....7....1

%e 11...21...15...1

%e 19...53...60...31...1

%e First three polynomials u(n,x): 1, 3+ x, 6 + 7x + x^2.

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;

%t v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;

%t Table[Expand[u[n, x]], {n, 1, z/2}]

%t Table[Expand[v[n, x]], {n, 1, z/2}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%] (* A210749 *)

%t Table[Expand[v[n, x]], {n, 1, z}]

%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

%t TableForm[cv]

%t Flatten[%] (* A210750 *)

%Y Cf. A210750, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 25 2012