|
%I #6 Mar 30 2012 18:58:13
%S 1,1,3,1,3,7,1,3,8,17,1,3,9,22,41,1,3,10,27,59,99,1,3,11,32,78,157,
%T 239,1,3,12,37,98,222,414,577,1,3,13,42,119,294,622,1084,1393,1,3,14,
%U 47,141,373,864,1722,2821,3363,1,3,15,52,164,459,1141,2500,4719
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208516; see the Formula section.
%F u(n,x)=u(n-1,x)+x*v(n-1,x),
%F v(n,x)=x*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 1...3
%e 1...3...7
%e 1...3...8...17
%e 1...3...9...22...41
%e First five polynomials v(n,x):
%e 1
%e 1 + 3x
%e 1 + 3x + 7x^2
%e 1 + 3x + 8x^2 + 17x^3
%e 1 + 3x + 9x^2 + 22x^3 + 41x^4
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t v[n_, x_] := x*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[%] (* A208516 *)
%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[%] (* A208517 *)
%Y Cf. A208514.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Feb 28 2012
|
