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%I #6 Mar 30 2012 18:58:16
%S 1,1,3,1,5,7,1,5,17,17,1,5,21,53,41,1,5,21,81,157,99,1,5,21,89,289,
%T 449,239,1,5,21,89,361,973,1253,577,1,5,21,89,377,1389,3133,3433,1393,
%U 1,5,21,89,377,1565,5085,9745,9273,3363,1,5,21,89,377,1597,6285
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209820; see the Formula section.
%C Let T(n,k) be the general term.
%C T(n,n): A001333
%C T(n,n-1): A088210
%C Row sums: A003561
%C Alternating row sums: 1,-2,3,-4,5,-6,7,-8,...
%C Limiting row: F(2), F(5),F(8),...where F=A000045 (Fibonacci numbers)
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,
%F v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...3
%e 1...5...7
%e 1...5...17...17
%e 1...5...21...53...41
%e First three polynomials u(n,x): 1, 1 + 3x, 1 + 5x + 7x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A209819 *)
%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[%] (* A209820 *)
%Y Cf. A209820, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 23 2012
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