cp's OEIS Frontend

A208911 Triangle of coefficients of polynomials u(n,x) jointly generated with A208912; see the Formula section.

%I A208911 #5 Mar 30 2012 18:58:14
%S A208911 1,1,2,1,6,4,1,12,14,8,1,20,32,38,16,1,30,60,110,90,32,1,42,100,250,
%T A208911 300,214,64,1,56,154,490,770,826,490,128,1,72,224,868,1680,2408,2128,
%U A208911 1110,256,1,90,312,1428,3276,5880,6888,5382,2474,512,1,110,420
%N A208911 Triangle of coefficients of polynomials u(n,x) jointly generated with A208912; see the Formula section.
%C A208911 For a discussion and guide to related arrays, see A208510.
%F A208911 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208911 v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A208911 where u(1,x)=1, v(1,x)=1.
%e A208911 First five rows:
%e A208911 1
%e A208911 1...2
%e A208911 1...6....4
%e A208911 1...12...14...8
%e A208911 1...20...32...38...16
%e A208911 First five polynomials u(n,x):
%e A208911 1
%e A208911 1 + 2x
%e A208911 1 + 6x + 4x^2
%e A208911 1 + 12x + 14x^2 + 8x^3
%e A208911 1 + 20x + 32x^2 + 38x^3 + 16x^4
%t A208911 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208911 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208911 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A208911 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208911 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208911 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208911 TableForm[cu]
%t A208911 Flatten[%]    (* A208911 *)
%t A208911 Table[Expand[v[n, x]], {n, 1, z}]
%t A208911 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208911 TableForm[cv]
%t A208911 Flatten[%]    (* A208912 *)
%Y A208911 Cf. A208912, A208510.
%K A208911 nonn,tabl
%O A208911 1,3
%A A208911 _Clark Kimberling_, Mar 03 2012