|
%I #6 Mar 30 2012 18:58:15
%S 1,1,1,2,2,1,2,5,3,1,3,6,9,4,1,3,11,13,14,5,1,4,12,28,24,20,6,1,4,19,
%T 34,59,40,27,7,1,5,20,62,80,110,62,35,8,1,5,29,70,164,166,188,91,44,9,
%U 1,6,30,115,200,376,314,301,128,54,10,1,6,41,125,365,496,776
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209556; see the Formula section.
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+v(n-1,x),
%F v(n,x)=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...1
%e 2...2...1
%e 2...5...3...1
%e 3...6...9...4...1
%e First three polynomials v(n,x): 1, 1 + x, 2 + 2x + x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t v[n_, x_] := 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[%] (* A209555 *)
%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[%] (* A209556 *)
%Y Cf. A209556, A208510.
%K nonn,tabl
%O 1,4
%A _Clark Kimberling_, Mar 10 2012
|
