cp's OEIS Frontend

A208520 Triangle of coefficients of polynomials u(n,x) jointly generated with A208521; see the Formula section.

%I A208520 #5 Mar 30 2012 18:58:13
%S A208520 1,1,1,1,3,2,1,6,6,2,1,10,12,10,4,1,15,20,30,20,4,1,21,30,70,60,28,8,
%T A208520 1,28,42,140,140,112,56,8,1,36,56,252,280,336,224,72,16,1,45,72,420,
%U A208520 504,840,672,360,144,16,1,55,90,660,840,1848,1680,1320,720,176
%N A208520 Triangle of coefficients of polynomials u(n,x) jointly generated with A208521; see the Formula section.
%F A208520 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208520 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A208520 where u(1,x)=1, v(1,x)=1.
%e A208520 First five rows:
%e A208520 1
%e A208520 1...1
%e A208520 1...3...2
%e A208520 1...6...6...2
%e A208520 1...10...12...10...4
%e A208520 First five polynomials u(n,x):
%e A208520 1
%e A208520 1 + x
%e A208520 1 + 3x + 2x^2
%e A208520 1 + 6x + 6x^2 + 2x^3
%e A208520 1 + 10x + 12x^2 + 10x^3 + 4x^4
%t A208520 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208520 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208520 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A208520 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208520 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208520 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208520 TableForm[cu]
%t A208520 Flatten[%]    (* A208520 *)
%t A208520 Table[Expand[v[n, x]], {n, 1, z}]
%t A208520 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208520 TableForm[cv]
%t A208520 Flatten[%]    (* A208521 *)
%Y A208520 Cf. A208521.
%K A208520 nonn,tabl
%O A208520 1,5
%A A208520 _Clark Kimberling_, Feb 28 2012