|
%I #5 Mar 30 2012 18:58:15
%S 1,2,3,3,5,7,4,8,16,17,5,12,30,47,41,6,17,50,99,134,99,7,23,77,181,
%T 315,373,239,8,30,112,302,628,968,1020,577,9,38,156,472,1128,2090,
%U 2898,2751,1393,10,47,210,702,1882,4020,6738,8495,7338,3363,11,57
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209701; see the Formula section.
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F v(n,x)=2x*u(n-1,x)+(x+1)v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2...3
%e 3...5....7
%e 4...8....16...17
%e 5...12...30...57...41
%e First three polynomials v(n,x): 1, 2 + 3x , 3 + 5x + 7x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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[%] (* A209701 *)
%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[%] (* A209702 *)
%Y Cf. A209701, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 12 2012
|
