A209579 - OEIS

%I #5 Mar 30 2012 18:58:15

%S 1,1,1,2,3,1,2,6,6,1,3,9,14,10,1,3,14,28,29,15,1,4,18,48,71,55,21,1,4,

%T 25,75,139,158,97,28,1,5,30,112,251,356,321,161,36,1,5,39,156,413,724,

%U 828,609,254,45,1,6,45,215,645,1321,1874,1782,1094,384,55,1,6

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209580; 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)=(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...1

%e 2...3....1

%e 2...6....6....1

%e 3...9....14...10...1

%e First three polynomials v(n,x): 1, 1 + x, 2 + 3x + 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_] := (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[%]   (* A209579 *)

%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[%]   (* A209580 *)

%Y Cf. A209580, A208510.

%K nonn,tabl

%O 1,4

%A _Clark Kimberling_, Mar 11 2012