|
%I #5 Mar 30 2012 18:58:13
%S 1,1,1,1,2,3,1,3,6,5,1,4,9,12,11,1,5,12,21,30,21,1,6,15,32,57,64,43,1,
%T 7,18,45,92,133,146,85,1,8,21,60,135,232,329,316,171,1,9,24,77,186,
%U 365,612,765,694,341,1,10,27,96,245,536,1015,1512,1801,1496,683
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208522; see the Formula section.
%F u(n,x)=u(n-1,x)+x*v(n-1,x),
%F v(n,x)=2x*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 1...2...3
%e 1...3...6...5
%e 1...4...9...12...11
%e First five polynomials u(n,x):
%e 1
%e 1 + x
%e 1 + 2x + 3x^2
%e 1 + 3x + 6x^2 + 5x^3
%e 1 + 4x + 9x^2 + 12x^3 + 11x^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_] := 2 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[%] (* A208522 *)
%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[%] (* A208523 *)
%Y Cf. A208523.
%K nonn,tabl
%O 1,5
%A _Clark Kimberling_, Feb 29 2012
|
